Apostila de Fisica EAD - Eletricidade, Magnetismo e Física Moderna

Eletricidade, Magnetismo & Fsica Moderna

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1. Captulo 1, A lei de Coulomb 2. Captulo 2, O campo Eltrico 3. Captulo 3, A lei de Gauss 4. Captulo 4, Potencial Eltrico 5. Captulo 5, Capacitncia e Capacitores 6. Captulo 6, Corrente & Resistncia 7. Captulo 7, Circuitos Eltricos 8. Captulo 8, O Campo Magntico 9. Captulo 9, A lei de Ampre 10. Captulo 10, A lei de Faraday 11. Captulo 11, Oscilaes Eletromagnticas 12. Captulo 12, Equaes de Maxwell

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Eletricidade & Magnetismo

Contedo do cursoq q q q q q q q q q q q

1. Captulo 1, A lei de Coulomb 2. Captulo 2, O campo Eltrico 3. Captulo 3, A lei de Gauss 4. Captulo 4, Potencial Eltrico 5. Captulo 5, Capacitncia e Capacitores 6. Captulo 6, Corrente & Resistncia 7. Captulo 7, Circuitos Eltricos 8. Captulo 8, O Campo Magntico 9. Captulo 9, A lei de Ampre 10. Captulo 10, A lei de Faraday 11. Captulo 11, Oscilaes Eletromagnticas 12. Captulo 12, Equaes de Maxwell

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Captulo 1

Captulo 1 - A LEI DE COULOMBContedo do Captuloq q q q q

Processos de Eletrizao Condutores e Isolantes Fora Eletrosttica Exemplo Exerccios




Captulo 2

Capitulo 2 - O CAMPO ELTRICOContedo do Captuloq q q q q

Ao a distancia Linhas de Fora Campo de um Dipolo Eltrico Exemplo Exerccios




Captulo 3 - A Lei de GaussCaptulo 3

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Fluxo do Campo Eltrico A lei de Gauss A lei de Gauss e a Lei de Coulomb Campo de uma Carga Puntiforme Distribuio Esfericamente Simtrica Esfera Condutora Esfera Dieltrica Distribuio Linear Infinita Plano Infinito de Cargas Exerccios




Captulo 4

Capitulo 4 - POTENCIAL ELTRICOContedo do Capituloq q q q q q q

Energia Potencial Potencial Potencial de uma carga puntiforme Potencial de um dipolo Potencial acelerador Gradiente de potencial Exerccios




Captulo 5

Captulo 5 CAPACITNCIA E CAPACITORESContedo do Captuloq q q q q q q q q q

Componentes Eltricos & Eletrnicos Definies Capacitor de placas paralelas Capacitor cilindrico Capacitor esferico Associao de capacitores Capacitores com dieltricos Armazenando energia num campo eltrico Exemplo Exerccios




Captulo 6

Captulo 6 - CORRENTE & RESISTNCIAContedo do Captuloq q q q q q q q

Modelo Microscpico Corrente Eltrica Resistncia, Resistividade e Conductividade Lei de Ohm Energia e Potencia Unidades no Sistema SI Exemplo Exerccios




Captulo 7

Captulo 7 - CIRCUITOS ELTRICOSContedo do Captuloq q q q q q q

Lei dos Ns & Lei das Malhas Lei das Malhas (Lei de Kirchhoff) Lei dos Ns Circuitos com mais de uma Malha Exemplo Circuito RC Srie Exerccios




Captulo 8

Captulo 8 - O CAMPO MAGNTICOContedo do Captuloq q q q q q q q q q

A fora de Lorentz A descoberta do Eletrn O Efeito Hall Movimento de uma carga num Campo Magntico Fora sobre uma Corrente Fora sobre uma Espira de Corrente Unidades Exemplo 8.1 Exemplo 8.2 Exerccios




Captulo 9

Captulo 9 - A LEI DE AMPREContedo do Captuloq q q q q q q

A Descoberta de Oersted Campo de um fio retilneo infinito Cilindro Infinito Interao entre fios infinitos paralelos Campo de um Solenide Exemplos Exerccios




Captulo 10

Captulo 10 - A LEI DE FARADAYContedo do Captuloq q q

Induo Eletromagntica Leis de Faraday e Lenz Exerccios




Captulo 11

Captulo 11 -OSCILAES ELETROMAGNTICASContedo do Captuloq q q q q

Indutncia Indutncia de um Solenide Auto-induo Circuito RL Densidade de Energia em Campos Eltricos e Magnticos Circuito LC Circuito RLC Freqncia Natural Exerccios

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Captulo 12

Captulo 12 - EQUAES DE MAXWELLContedo do Captuloq q

Equaes de Maxwell Exerccios



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CAPES / MEC

Sbado, 13 de maro de 2004

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INFORMAES Pr-Coleta Professor Est disponvel o Pr-Coleta Professor 2.5. POSSE Jorge Almeida Guimares toma posse na presidncia da Capes Programa de Qualificao Institucional - PQI Acesse o formulrio referente ao Relatrio de Atividades Cincias Agrrias Acesse os critrios de avaliao para a grande rea (2001-2003)e os critrios especficos para avaliao de cursos novos e programas de psgraduao entre Instituio de Ensino Superior (IES) e Instituto de Pesquisa (IP). Coleta de Dados A Diretoria de Avaliao informa que o prazo de entrega dos dados da Coleta relativos a 2003, assim como o re-envio dos dados de 2001 e 2002 dia 31 de maro de 2004, no havendo possibilidade de adiamento. Trata-se de um ano de Avaliao que atribuir conceitos e o cronograma j estabelecido para a realizao do processo deve ser seguido. Aplicativo A Coordenao de Acompanhamento e Avaliao disponibiliza a cartaconsulta sobre proposta de cursos de mestrado e doutorado. Comisso Mista Capes/CNPq Apresentao do Relatrio Final (Sumrio Executivo)

CAPES ALERTA Programa PICDT Informamos aos bolsistas do Programa PICDT, que os pagamentos referentes aos meses de Janeiro e Fevereiro/2004 j esto sendo regularizados. Entrevista de Candidatos a Bolsa de Doutorado no Exterior CAPES realiza a ltima etapa da seleo dos candidatos a bolsas de doutorado no exterior. Mestrados e Doutorados sem validade. So consideradas ilegais, no Brasil, as atividades acadmicas das instituies de ensino estrangeiras que no tenham sido reconhecidas pelo MEC. Leia a ntegra da notcia. Resoluo CNE/CES 001/2001 alterada pela Resoluo CNE/CES 24/2002. Novos prazos para solicitao de reconhecimento dos programas e necessidade de autorizao do MEC para instalao de convnios entre IES brasileiras e estrangeiras que ofertem mestrados/doutorados associados so as novidades. Confira o texto.

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Antes de Comenar

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Introduo Exigncias de hardware e software

IntroduoO curso est formatado de acordo com a pedagogia construtivista, a partir de uma abordagem baseada na soluo de problemas. O contedo distribudo em 12 captulos. Para acess-los, diriga-se ao sumrio O contedo explorado atravs de uma variedade de objetos de aprendizagem interativos. Ao final apresenta-se uma lista de exerccios. Alguns objetos de aprendizagem foram extraidos ou adaptados dos seguintes autores, que permitiram seu uso nas condies desta disciplina. Wolfgang Christian, editor da pgina Physlets. Michael W. Davidson, editor da pgina Molecular Expressions: Electricity and Magnetism Walter Fendt, editor da pgina Java Applets on Physics

Exigncias de hardware e softwarePara maior eficincia, convm observar os seguintes aspectos: 1. Nestcape Navigator ou Microsoft Internet Explorer so os navegadores mais apropriados. Eles podem ser obtidos livremente na web. 2. Para as animaes, seu navegador tem que suportar Java.

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Antes de Comenar

PC com procesador de 90 MHz ou superior. 16 Mb RAM ou superior. Monitor SVGA ou compatible. Resoluo mnima de 800x600 (recomendado 1024x768) pixels. Modem de 28.8 kbps ou superior

Exigncias de softwareNestcape Navigator (Verso 4.0 ou superior). Use este endereo http://www.nestcape.com para carreg-lo. Microsoft Internet Explorer (Verso 4.0 ou superior). Use este endereo http://www.microsoft.com/ie/ para carreglo. Plugin de Java - Applets http://www.java.com/en/download/windows_automatic.jsp.

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Physlets Home Page

Welcome to the Physlets resource page. Physlets, Physics Applets, are small flexible Java applets designed for science education. You do not need to become a Java expert in order to use Physlets. The links on the right contain tutorials, download instructions, and example problems to help you use Physlets in your teaching.Physlets run on the Mac using OS X Panther and the latest Safari browser.q

For a CD containing over 800 ready to run Physlet-based Illustrations, Exercises, and Problems see the Physlet Physics book. For an introduction to scripting see thee Physlet book. This book will soon be available in Spanish! For a discussion of how to use Physlets with Just-in-Time Teaching see the JiTT book. To learn more about Physlets you may want to:

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Attend a Physlet workshop. Preview Physlet Physics, a book of ready to run Physlet-based Illustrations, Explorations, and Problems. Search the Kaiserslautern Physlet database. Sign up on the Physlet list-server.

The Physics Teacher recently contained a feature article describing the Optics Bench Physlet. Examples from this article are available on the the Physlet Resource site.

The applet on the right is a Physlet. It simulates the relativistic and nonrelativistic Doppler effect. Send questions or comments about this site to Wolfgang Christian: [email protected]

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Physlets Home Page

Since 2/1/2001 This PIRA Webring site is owned by Wolfgang Christian. < prev | List Sites | next >

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Molecular Expressions: Images from the Microscope

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Welcome to the Molecular Expressions website featuring our acclaimed photo galleries that explore the fascinating world of optical microscopy. We are going where no microscope has gone before by offering one of the Web's largest collections of color photographs taken through an optical microscope (commonly referred to as "photo-micro-graphs"). Visit our Photo Gallery for an introductory selection of images covering just about everything from beer and ice cream to integrated circuits and ceramic superconductors. These photographs are available for licensing to commercial, private, and non-profit institutions.

Powers of Ten - Soar through space starting at 10 million light years away from the Milky Way down through to a single proton in Florida in decreasing powers of ten (orders of magnitude). Explore the use of exponential notation to understand and compare the size of things in our world and the universe. Olympus FluoView Laser Scanning Confocal Microscopy - The new Olympus FluoViewTM FV1000 is the latest in point-scanning, point-detection, confocal laser scanning microscopes designed for today's intensive and demanding biological research investigations. Excellent resolution, bright and crisp optics, and high efficiency of excitation, coupled to an intuitive user interface and affordability are key characteristics of this state-of-the-art optical microscopy system. Purchase Nikon's Small World 2004 Calendar - The Nikon Small World 2004 Calendar is printed in full color on 8.5 x 11 semi-gloss paper and spiral bound for mounting on the wall. Included in the calendar are the top 20 prize winners and thumbnail images from all of the 17 honorable mentions. Winning entries included several images of rat and mouse brain cells, nematode worms, a computer chip, muscle cells, a diatom, snowflakes, plant hair cells, thin films, and chemical crystals. This year's contest drew entrants from 46 countries, as well as from a diverse range of academic and professional disciplines. Winners came from such fields as chemistry, biology, materials research, botany, and biotechnology. Microscope: Basics and Beyond (50 pages; 20.7 Mbytes) - Download the latest PDF edition of Mortimer Abramowitz's renowned introduction to optical microscopy in full color. The volume covers all of the important basic concepts, ranging from simple magnifiers to complex compound microscopes, including illumination, objectives, eyepieces, condensers, aberration, Khler illumination, resolution, numerical aperture, and depth of field. Numerous appendices review focusing of the microscope and oil immersion, and contain useful numbers, formulas, and a short bibliography. The Olympus MIC-D Digital Microscope - Olympus has thrown the doors open to a new era in optical microscopy education with the introduction of the MIC-D inverted digital microscope. Designed specifically for a wide spectrum of applications ranging

The Galleries: Photo Gallery Silicon Zoo Pharmaceuticals Chip Shots Phytochemicals DNA Gallery Microscapes Vitamins Amino Acids Birthstones Religion Collection Pesticides BeerShots Cocktail Collection Screen Savers Win Wallpaper Mac Wallpaper Movie Gallery

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from basic classroom instruction to more advanced laboratory analysis, this versatile microscope features a palette of contrast enhancing techniques that rival many research-level instruments. Nikon MicroscopyU - The MicroscopyU website is designed to provide an educational forum for all aspects of optical microscopy, digital imaging, and photomicrography. Together with the scientists and programmers at Molecular Expressions, Nikon microscopists and engineers are providing the latest state-of-theart information in microscope optics and imaging technology including specialized techniques such as fluorescence, differential interference contrast (DIC), phase contrast, reflected light microscopy, and microscopy of living cells. We invite you to explore MicroscopyU and discover more about the exciting world of optics and microscopy. Burgers 'n Fries - Join us for a microscopic examination of America's culinary favorite: the ubiquitous hamburger and French fries. Discover how this delightful classic is just as beautiful as it is tasty. Chemical Crystals - Chemical compounds can exist in three basic phases, gaseous, liquid, or solid. Gases consist of weakly bonded atoms and expand to fill any available space. Solids are characterized by strong atomic bonding and have a rigid shape. Most are crystalline, having a three-dimensional periodic atomic arrangement. Some, such as glass, lack this periodic arrangement and are noncrystalline, or amorphous. Liquids have characteristics that fall in between gases and solids. This cinemicrographic collection presents time-lapse movies of various chemical compounds as they change physical states. Scanning Electron Microscopy - We have teamed up with award-winning electron microscopist Dennis Kunkel to produce a virtual Scanning Electron Microscope (vSEM). Visitors can adjust the focus, contrast, and magnification of microscopic creatures viewed at thousands of times their actual size. Laser Scanning Confocal Microscopy - (approximately a 30 second download on 28.8K modems) Several methods have been developed to overcome the poor contrast inherent with imaging thick specimens in a conventional microscope. Specimens having a moderate degree of thickness (5 to 15 microns) will produce dramatically improved images with either confocal or deconvolution techniques. The thickest specimens (20 microns and above) will suffer from a tremendous amount of extraneous light in out-of-focus regions, and are probably best-imaged using confocal techniques. This tutorial explores imaging specimens through serial z-axis optical sections utilizing a virtual confocal microscope. Stereoscopic Zoom Microscopy - Many stereoscopic microscopes feature the ability to perform a continuous magnification change by means of a zoom lens system placed between the objective and the eyepieces. Explore zoom magnification, focus, and illumination intensity in stereoscopic microscopes with this interactive Flash tutorial. Java-powered QX3 Computer Web Microscope - This virtual QX3 microscope is broadcasting images over the Web at 20 frames/second, which can be viewed in a specially designed Java client run through your Web browser at frame rates up to 18 frames/second. No additional software is needed, but don't try this unless you have a fast connection (10 Mbits/sec Ethernet or higher). With this software, you canhttp://micro.magnet.fsu.edu/index.html (2 de 11) [13/03/2004 16:16:54]


capture single digital images, record movies, and perform time-lapse cinematography experiments. Museum of Microscopy - Featuring 3-D Studio Max drawings of ancient microscopes, this unique gallery explores many of the historic microscopes made during the last four centuries. Visit the gallery and download a copy of our Windows screen saver containing selected images of these beautiful microscopes. Silicon Zoo - This popular gallery features images of cartoon characters and other doodling placed onto computer chips by their designers. Featured Microscopist - Our featured microscopist for Spring 2002 is noted Dutch photomicrographer Loes Modderman. Born in Amsterdam in 1944, Modderman received her first microscope by age 13 and has never lost her sense of wonder at the minute beauties available with this instrument. Many years ago, Loes initiated a series of chemical crystallization experiments, which allowed her to meld longtime interests in nature, art, science, and photography to form her abstract photomicrographs into a colorful celebration of form and structure. A wide spectrum of these photomicrographs are featured in this gallery. Cell and Virus Structure - Although the human body contains over 75 trillion cells, the majority of life forms exist as single cells that perform all the functions necessary for independent existence. Most cells are far too small to be seen with the naked eye and require the use of high-power optical and electron microscopes for careful examination. Fluorescence Microscopy Digital Image Gallery - Featuring specimens collected from a wide spectrum of disciplines, the fluorescence gallery contains a variety of examples using both specific fluorochrome stains and autofluorescence. Images were captured utilizing either a Nikon DXM 1200 digital camera, an Optronics MagnaFire Peltier-cooled camera, or classical photomicrography on film with Fujichrome Provia 35 millimeter transparency film. Pond Life - Freshwater ponds provide a home for a wide variety of aquatic and semiaquatic plants, insects, and animals. The vast majority of pond inhabitants, however, are invisible until viewed under the microscope. Beneath the placid surface of any pond is a microscopic metropolis bustling with activity as tiny bizarre organisms pursue their lives; locomoting, eating, trying not to be eaten, excreting, and reproducing. In this collection of digital movies, observe the activities of microscopic organisms taken from a typical North Florida pond. Concepts in Digital Imaging Technology - Explore the basic concepts in digital imaging with our illustrated discussions and interactive tutorials. Topics covered include CCD operation, image capture, digital manipulation of images and a wide spectrum of other issues in this emerging field. Science, Optics & You - Explore our science curriculum package being developed for teachers, students, and parents. Activities are designed to promote the asking and answering of questions related to light, color, and optics. The program begins with basic information about lenses, shadows, prisms, and color, leading up to the use of sophisticated instruments scientists use to help them understand the world. Intel Play QX3 Computer Microscope - Take a moment to visit our in-depthhttp://micro.magnet.fsu.edu/index.html (3 de 11) [13/03/2004 16:16:54]


discussion of this incredible toy microscope. Included topics are the QX3 hardware (microscope), interactive microscope software, suggested specialized techniques, and digital image galleries from the QX3 microscope. Creative Photomicrography - By employing multiple exposure photomicrography, we have succeeded in generating a series of unusual micrographs which we have termed microscapes. These micrographs are intended to resemble surrealistic/alien landscapes.

10 Best Interactive Java Tutorials Digital Image Processing Interactive Java Tutorials - Explore the basic concepts of digital image processing applied to specimens captured in the microscope. Techniques reviewed include contrast, color balance, spatial resolution, image sampling frequency, geometric transformation, averaging, measurements, histogram manipulation, convolution kernels, filtering digital images, compression, noise reduction, and binary digital images. Full-Frame CCD Operation - Having the simplest architecture and being the easiest devices to build and operate, full-frame charged coupled devices (CCDs) feature high-density pixel arrays capable of producing digital images with the highest resolution currently available. Explore how images are captured and transferred to serial output registers with this interactive Java tutorial. Intel Play QX3 Computer Microscope Simulator - Discover how the hardware and software of this amazing "toy" microscope work together to produce images that you can digitally manipulate with a personal computer. Geometrical Construction of Ray Diagrams - A popular method of representing a train of propagating light waves involves the application of geometrical optics to determine the size and location of images formed by a lens or multi-lens system. This tutorial explores how two representative light rays can establish the parameters of an imaging scenario. Reflected Light Confocal Microscopy - Explore microscopy of integrated circuits using real-time confocal observations at a resolution of 0.18 microns with this interactive Java tutorial. Building A Charged Coupled Device - Explore the steps utilized in the construction of a charged coupled device (CCD) as a portion of an individual pixel gate is fabricated on a silicon wafer simultaneously with thousands or even millions of neighboring elements. Astigmatism - Astigmatism aberrations are similar to comatic aberrations, however these artifacts are not as sensitive to aperture size and depend more strongly on the oblique angle of the light beam. The aberration is manifested by the off-axis image of a specimen point appearing as a line or ellipse instead of a point. Video Signal Generation - A video signal is a recoverable train of electrical impulses generated by scanning a two-dimensional image produced by the optical train of a microscope. The image is sequentially scanned in narrow strips andhttp://micro.magnet.fsu.edu/index.html (4 de 11) [13/03/2004 16:16:54]


combined to produce the final signal. This interactive tutorial explores the relationship between the microscope image, scan lines, and the video signal. Airy Pattern Formation - When an image is formed in the focused image plane of an optical microscope, every point in the specimen is represented by an Airy diffraction pattern having a finite spread. This occurs because light waves emitted from a point source are not focused into an infinitely small point by the objective, but converge together and interfere near the intermediate image plane to produce a three-dimensional Fraunhofer diffraction pattern. Fluorescence Microscope Light Pathways - This interactive tutorial explores illumination pathways in the Olympus BX51 research-level upright microscope. The microscope drawing presented in the tutorial illustrates a cut-away diagram of the Olympus BX51 microscope equipped with a vertical illuminator and lamphouses for both diascopic (tungsten-halogen) and epi-fluorescence (mercury arc) light sources. Sliders control illumination intensity and enable the visitor to select from a library of five fluorescence interference filter combinations that have excitation values ranging from the near ultraviolet to long-wavelength visible light. Condenser Alignment - This tutorial demonstrates how the condenser is centered in the optical path and the size of the field diaphragm opening is determined when adjusting a microscope for proper Khler illumination.

New Microscopy Primer EntriesIf you need information about optical microscopy, how to set up a microscope, or how to take photographs with a microscope, then visit our Microscopy Primer for a detailed discussion.

Basic Concepts in Digital Image Processing - Digital image processing enables the reversible, virtually noise-free modification of an image in the form of a matrix of integers instead of the classical darkroom manipulations or filtration of timedependent voltages necessary for analog images and video signals. Even though many image processing algorithms are extremely powerful, the average user often applies operations to digital images without concern for the underlying principles behind these manipulations. The images that result from careless manipulation are often severely degraded or otherwise compromised with respect to those that could be produced if the power and versatility of the digital processing software were correctly utilized. Introduction to CMOS Image Sensors - CMOS image sensors are designed with the ability to integrate a number of processing and control functions, which lie beyond the primary task of photon collection, directly onto the sensor integrated circuit. These features generally include timing logic, exposure control, analog-todigital conversion, shuttering, white balance, gain adjustment, and initial image processing algorithms. Inexpensive CMOS image sensors are entering the field of optical microscopy in educational instruments that combine acceptable optical quality with user-friendly control and imaging software packages. Introduction to Prisms and Beamsplitters - Prisms and beamsplitters are essential components that bend, split, reflect, and fold light through the pathways of both simple and sophisticated optical systems. Cut and ground to specific tolerances and exact angles, prisms are polished blocks of glass or otherhttp://micro.magnet.fsu.edu/index.html (5 de 11) [13/03/2004 16:16:54]


transparent materials that can be employed to deflect or deviate a light beam, rotate or invert an image, separate polarization states, or disperse light into its component wavelengths. Many prism designs can perform more than one function, which often includes changing the line of sight and simultaneously shortening the optical path, thus reducing the size of optical instruments. Stereomicroscopy - Stereomicroscopes have characteristics that are valuable in situations where three-dimensional observation and perception of depth and contrast is critical to the interpretation of specimen structure. These instruments are also essential when micromanipulation of the specimen is required in a large and comfortable working space. The wide field of view and variable magnification displayed by stereomicroscopes is also useful for construction of miniature industrial assemblies, or for biological research that requires careful manipulation of delicate and sensitive living organisms. Basic Microscope Ergonomics - In order to view specimens and record data, microscope operators must assume an unusual but exacting position, with little possibility to move the head or the body. They are often forced to assume an awkward work posture such as the head bent over the eye tubes, the upper part of the body bent forward, the hand reaching high up for a focusing control, or with the wrists bent in an unnatural position. Image Formation - In the optical microscope, image formation occurs at the intermediate image plane through interference between direct light that has passed through the specimen unaltered and light diffracted by minute features present in the specimen. The image produced by an objective lens is conjugate with the specimen, meaning that each image point at the intermediate plane is geometrically related to a corresponding point in the specimen. Basic Properties of Digital Images - Continuous-tone images are produced by analog optical and electronic devices, which accurately record image data by several methods, such as a sequence of electrical signal fluctuations or changes in the chemical nature of a film emulsion that vary continuously over all dimensions of the image. In order for a continuous-tone or analog image to be processed or displayed by a computer, it must first be converted into a computer-readable form or digital format. This process applies to all images, regardless the origin and complexity, and whether they exist as black and white (grayscale) or full color. A digital image is composed of a rectangular (or square) pixel array representing a series of intensity values and ordered through an organized (x,y) coordinate system. Introduction to Confocal Microscopy - Confocal microscopy offers several advantages over conventional optical microscopy, including controllable depth of field, the elimination of image degrading out-of-focus information, and the ability to collect serial optical sections from thick specimens. The key to the confocal approach is the use of spatial filtering to eliminate out-of-focus light or flare in specimens that are thicker than the plane of focus. There has been a tremendous explosion in the popularity of confocal microscopy in recent years, due in part to the relative ease with which extremely high-quality images can be obtained from specimens prepared for conventional optical microscopy, and in its great number of applications in many areas of current research interest. Electronic Imaging Detectors - The range of light detection methods and the widehttp://micro.magnet.fsu.edu/index.html (6 de 11) [13/03/2004 16:16:54]


variety of imaging devices currently available to the microscopist make the selection process difficult and often confusing. This discussion is intended to aid in understanding the basics of light detection and to provide a guide for selecting a suitable detector for specific applications in optical microscopy. Troubleshooting Classical and Digital Photomicrography - Photography through the microscope is undergoing a transition from film to digital imaging. New digital technologies are producing higher resolution micrographs, but the quality still falls short of that obtainable with film. Microscope configuration errors represent the greatest obstacle to quality photomicrographs, followed by errors in filter selection, film choice, aberration, dirt and debris, and processing mistakes. Oblique or Anaxial Illumination - Achieving conditions necessary for oblique illumination, which has been employed to enhance specimen visibility since the dawn of microscopy, can be accomplished by a variety of techniques with a simple transmitted optical microscope. Perhaps the easiest methods are to offset a partially closed condenser iris diaphragm or the image of the light source. In former years, some microscopes were equipped with a condenser having a decenterable aperture iris diaphragm. The device was engineered to allow the entire iris to move off-center in a horizontal plane so that closing the circular diaphragm opening would result in moving the zeroth order to the periphery of the objective rear focal plane. In advanced models, the entire diaphragm was rotatable around the axis of the microscope so that oblique light could be directed toward the specimen from any azimuth to achieve the best desired effect for a given specimen. Multiphoton Excitation Microscopy - Multiphoton fluorescence microscopy is a powerful research tool that combines the advanced optical techniques of laser scanning microscopy with long wavelength multiphoton fluorescence excitation to capture high-resolution, three-dimensional images of specimens tagged with highly specific fluorophores.

Best of the Silicon Zoo Flying Osprey - A Hewlett-Packard design team headed by Howard Hilton in Lake Stevens, Washington was responsible for placing what is perhaps the World's smallest rendition of an osprey on a decimation filter integrated circuit utilized in signal analyzer instruments. Snoopy - The silicon version of Snoopy illustrated in this section was discovered by Richard Piotter of New Ulm, Minnesota, who also loaned the 4-inch wafer (made by a 1980s-era semiconductor company named Trilogy) from which the image is derived. The Con Artist - We found this guy in a trench coat trying to hock some fake Rolex watches (that are probably "hot") on a Hewlett-Packard PA-RISC microprocessor. Housed near the clock circuitry on the chip, the silicon artwork signifies a pun on higher-end microprocessor clock systems that utilize a more complex feature set. Pac-Man - A silicon version of the famous game character was photographed gobbling the initials GAAS (gallium arsenide) on a TEMIC Semiconductors silicongermanium radio frequency integrated circuit.



Milhouse Van Houten - Simpson's cartoon character Milhouse was spotted on a Silicon Image Sil154CT64 digital transmitter integrated circuit. Godzilla - This mythical Japanese creature was discovered lurking on a pad within the Silicon Graphics MIPS R10000 microprocessor (this chip is sure crowded with silicon creatures). Tux, the Linux Penguin - Tux is nesting within the pad ring on an integrated circuit of unknown function (perhaps the latest new microprocessor designed to run the Linux operating system). Starship USS Enterprise - This famous Star Trek icon was discovered on a Texas Instruments bipolar logic integrated circuit. The Pepsi Generation - Perhaps the smallest soft drink advertisement ever created, this 750 micron Pepsi commercial was discovered on a Hewlett-Packard CPU-support chip. The Rolex - An intricate bitmap-like pattern of vias (interconnect shafts) was used to construct this incredible likeness of a Rolex wristwatch. The Stay Puft Marshmallow Man - Coming to you from "GhostBusters", the Stay Puft Marshmallow Man was cooked in a frying pan within the circuitry of a Weitek math coprocessor designed in 1988. Thor: God of Thunder - Probably the best silicon artwork we have yet seen, this image was discovered on a Hewlett-Packard graphics chip. The Chip Smurf - An orange silicon Smurf is pulling a wagon containing the copyright symbol around the pad ring on a Siemens integrated circuit of unknown function.

New Photo Gallery Entries Observing Mitosis with Fluorescence Microscopy - Mitosis, a phenomenon observed in all higher eukaryotes, is the mechanism that allows the nuclei of cells to split and provide each daughter cell with a complete set of chromosomes during cellular division. This, coupled with cytokinesis (division of the cytoplasm), occurs in all multicellular plants and animals to permit growth of the organism. Digital imaging with fluorescence microscopy is becoming a powerful tool to assist scientists in understanding the complex process of mitosis on both a structural and functional level. Brightfield Microscopy Digital Image Gallery - Brightfield illumination has been one of the most widely used observation modes in optical microscopy for the past 300 years. The technique is best suited for utilization with fixed, stained specimens or other kinds of samples that naturally absorb significant amounts of visible light. Images produced with brightfield illumination appear dark and/or highly colored against a bright, often light gray or white, background. This digital image gallery explores a variety of stained specimens captured with an Olympus BX51 microscope coupled to a 12-bit QImaging Retiga camera system.http://micro.magnet.fsu.edu/index.html (8 de 11) [13/03/2004 16:16:54]


Polarized Light Microscopy Digital Image Gallery - As a contrast-enhancing optical technique, polarized light microscopy is unsurpassed in the magnificent array of colors and beautiful textures generated through interference between orthogonal wavefronts at the analyzer. Useful for observation of mineral thin sections, hairs, fibers, particles, bones, chemical crystals, polymers, and a wide variety of other specimens, polarized light can be employed for both quantitative as well as qualitative investigations. Visit this gallery to observe how polarized light can be of advantage in the observation of specimens that would otherwise exhibit poor contrast and be difficult to distinguish from the background. Differential Interference Contrast Digital Image Gallery - Thin unstained, transparent specimens are excellent candidates for imaging with classical differential interference (DIC) microscopy techniques over a relatively narrow range (plus or minus one-quarter wavelength) of bias retardation. The digital images presented in this gallery represent a wide spectrum of specimens, which vary from unstained cells, tissues, and whole organisms to both lightly and heavily stained thin and thick sections. In addition, several specimens exhibiting birefringent character are included to demonstrate the kaleidoscopic display of color that arises when anisotropic substances are imaged with this technique. Confocal Microscopy Digital Image Gallery - Scroll through serial optical sections from a wide variety of specimens, including tissue culture cells, thin and thick sections, and entire organisms, in this Java-powered image gallery. The DNA Gallery - DNA undergoes a number of liquid crystalline phase transitions both in vitro and in vivo. This gallery explores the microscopic textures exhibited by various liquid crystalline DNA phases and their transition states. The Phytochemical Collection - Acclaimed by Newsweek as being "better than Vitamins", phytochemicals are blazing a new frontier in the arena of cancerprevention research. Explore the beautiful crystalline patterns displayed by phytochemicals captured in polarized light. Intel Play QX3 Microscope Galleries - Check out digital images captured with this incredible microscope using contrast enhancing techniques such as polarized light, darkfield, brightfield, and Rheinberg illumination. Phase Contrast Gallery - By "converting" phase objects such as living material into amplitude specimens, phase contrast illumination allows scientists to see details in unstained and/or living objects with great clarity and resolution. Explore the wide spectrum of biological specimens presented in this gallery of digital images. Hoffman Modulation Contrast Gallery - The modulation contrast technique takes advantage of optical phase gradients to yield a pseudo three-dimensional effect on images seen in the microscope. Darkfield Microscopy Gallery - Darkfield illumination provides good contrast for specimens that are often lacking in sufficient detail using other illumination techniques. Dinosaur Bones - Photographs of thin sections made from bones left behind by dinosaurs that have been extinct for over 70 million years.http://micro.magnet.fsu.edu/index.html (9 de 11) [13/03/2004 16:16:54]


Electricity & Magnetism Interactive Java Tutorials Electricity & Magnetism Interactive Java Tutorials - Visit our interactive tutorials on electricity and magnetism to explore how these two forces of nature operate in our everyday lives. Building A Transistor - Explore how an individual Field Effect (FET) transistor is fabricated on a silicon wafer simultaneously with millions of its neighbors. Pulsed Magnets - Pulsed magnets are among the strongest magnets in the world, and come in two forms: destructive and non-destructive. Of these two, nondestructive magnets are more suited towards scientific research, as they can reach some of the highest magnetic fields experimentally possible. This applet demonstrates how a non-destructive short pulse magnet works, and shows the relative field strengths generated. How a Compact Disc Works - This tutorial explores how a laser beam is focused onto the surface of a spinning compact disc, and how variations between pits and lands on the disc surface affect how light is either scattered by the disc surface or reflected back into a detector. Electrophoresis - Explore how electrical potential can cause migration and separation of macromolecules according to size in a cross-linked gel.

In the upcoming weeks and months, we will be adding more galleries, interactive Java tutorials, Silicon Zoo artwork, Chip Shots and new entries for the image collections on our website so please come back from time to time and check out our new additions. BACK TO THE TOP

Questions or comments? Send us an email. 1995-2004 by Michael W. Davidson and The Florida State University. All Rights Reserved. No images, graphics, software, scripts, or applets may be reproduced or used in any manner without permission from the copyright holders. Use of this website means you agree to all of the Legal Terms and Conditions set forth by the owners. This website is maintained by our Graphics & Web Programming Team in collaboration with Optical Microscopy at the National High Magnetic Field Laboratory. Last modification: Thursday, Mar 04, 2004 at 09:44 AM Access Count Since September 12, 1995: 3011717 Microscopes provided by:




Java Applets on Physics (Java 1.4)

Java Applets on PhysicsWalter Fendt

(Java 1.4, 46 English version www.walter-fendt.de/ph14e applets, 2004-0311)www.walter-fendt.de/ph11e (Java 1.1, 41 applets, 2002-12-27)

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MechanicsMotion with Constant Acceleration Equilibrium of Three Forces Resolution of a Force into Components Pulley System Lever Principle Inclined Plane Newton's Second Law Experiment Projectile Motion Elastic and Inelastic Collision Newton's Cradle Carousel (Centripetal Force) Kepler's First Lawhttp://www.walter-fendt.de/ph14e/ (1 de 3) [13/03/2004 16:17:14]

11/02/2000 - 01/18/2003 03/11/2000 - 01/18/2003

Resultant of Forces (Addition of Vectors) 11/02/1998 - 01/18/200305/30/2003 - 07/01/2003 03/24/1998 - 01/18/2003 11/02/1997 - 01/18/2003 02/24/1999 - 01/18/2003 12/23/1997 - 01/18/2003 09/13/2000 - 01/18/2003 11/07/1998 - 01/18/2003 11/04/1997 - 01/18/2003 03/10/1999 - 01/18/2003 03/25/2000 - 01/18/2003


Kepler's Second Law Hydrostatic Pressure in Liquids Buoyant Force in Liquids

04/04/2000 - 01/18/2003 02/03/1999 - 01/18/2003 04/19/1998 - 01/18/2003

Oscillations and WavesSimple Pendulum Spring Pendulum Coupled Pendula Forced Oscillations (Resonance) Beats05/21/1998 - 01/18/2003 05/24/1998 - 01/18/2003 07/05/1998 - 01/18/2003 09/11/1998 - 01/18/2003 10/21/2001 - 01/18/2003

Standing Wave (Explanation by Superposition with the Reflected New! (11/02/2003) Wave) Standing Longitudinal Waves Interference of two Circular or Spherical Waves Doppler Effect06/08/1998 - 01/18/2003 05/22/1999 - 01/18/2003 02/25/1998 - 01/18/2003

ElectrodynamicsMagnetic Field of a Bar Magnet Lorentz Force Direct Current Electrical Motor Generator Ohm's Law Combinations of Resistors Simple AC Circuits Electromagnetic Oscillating Circuit Electromagnetic Wave04/20/2001 - 01/18/2003

Magnetic Field of a Straight Current-Carrying Wire 09/18/2000 - 01/18/200306/01/1998 - 01/18/2003 11/29/1997 - 01/18/2003 05/08/1998 - 01/18/2003 11/23/1997 - 11/27/2003 09/11/2002 - 07/04/2003 06/13/1998 - 01/18/2003 12/08/1999 - 01/18/2003 09/20/1999 - 01/18/2003

OpticsRefraction of Light Reflection and Refraction of Light Waves (Explanation by Huygens' Principle) Refracting Astronomical Telescope Interference of Light at a Double Slit12/20/1997 - 01/18/2003 03/05/1998 - 11/01/2003 03/08/2000 - 01/18/2003 10/07/2003 - 11/01/2003

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Diffraction of Light by a Single Slit

10/11/2003 - 11/01/2003

ThermodynamicsSpecial Processes of an Ideal Gas 12/25/1999 - 01/18/2003

Theory of RelativityTime Dilation 11/15/1997 - 01/18/2003

Physics of AtomsPhotoelectric Effect02/20/2000 - 01/18/2003

Bohr's Theory of the Hydrogen Atom 05/30/1999 - 01/18/2003

Nuclear PhysicsRadioactive Decay Series 07/20/1998 - 01/18/2003 Law of Radioactive Decay 07/16/1998 - 01/18/2003

Walter Fendt, March 11, 2004

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1.2 PROCESSOS DE ELETRIZAO

Captulo 1 - A LEI DE COULOMBPROCESSOS DE ELETRIZAOEssencialmente, existem dois tipos de portadores de carga eltrica: prtons (+) e eltrons(-). Em condies de equilbrio, qualquer material eletricamente neutro, contendo igual nmero de prtons e eltrons. Um material eletricamente positivo quando tem excesso de prtons, ou falta de eltrons. Da mesma forma, ele ser negativamente carregado se tiver um excesso de eltrons. Um material pode ser eletrizado atravs de dois processos:r r

Eletrizao por atrito Eletrizao por induo

Eletrizao por atrito ocorre quando materiais no condutores so atritados uns contra outros. Nesse processo, um dos materiais perde eltrons e outro ganha, de modo que um tipo de material fica positivo e outro fica negativo. Uma experincia simples consiste em carregar um pente passando-o vrias vezes no cabelo. A comprovao de que ele ficou carregado obtida atraindo-se pequenas partculas, por exemplo, de p de giz. A figura ilustra as etapas essenciais do processo de eletrizao por induo. Nahttp://www.if.ufrgs.br/tex/fis142/mod01/m_s01.html (1 de 2) [13/03/2004 16:18:14]

1.2 PROCESSOS DE ELETRIZAO

ilustrao, tem-se inicialmente um corpo carregado e outro descarregado ( para que o processo seja factvel, este corpo deve ser condutor). A aproximao do corpo positivamente carregado atrai as cargas negativas do corpo eletricamente neutro. A extremidade prxima ao corpo carregado fica negativa, enquanto a extremidade oposta fica positiva. Mantendo-se o corpo carregado prximo, ligase o corpo eletricamente neutro terra. Eltrons subiro da terra para neutralizar o excesso de carga positiva. Cortando-se a ligao terra, obtm-se um corpo negativamente carregado.

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1.3 A LEI DE COULOMB

Capitulo 1- A LEI DE COULOMBCondutores e IsolantesNo contexto do eletromagnetismo, podemos classificar os materiais em:r r r r

Condutores Isolantes (ou dieltricos) Semicondutores Supercondutores.

Para o momento, vamos nos deter apenas nos condutores e nos dieltricos. Como os nomes sugerem, um material condutor tem facilidade para conduzir a eletricidade, enquanto um dieltrico no conduz a eletricidade. Na verdade, seria melhor dizer que um dieltrico quase no conduz a eletricidade. H circunstncias (veremos mais tarde) em que ele tambm conduz. Podemos dizer, numa linguagem bastante simples, que um dieltrico diferente de um condutor porque este tem eltrons livres, que se encarregam de conduzir a eletricidade. Assim, quando uma certa quantidade de carga eltrica colocada num material dieltrico, ela permanece no local em que foi colocada. Ao contrrio, quando esta carga colocada num condutor, ela tender a se distribuir at que o campo no interior do material seja nulo.

http://www.if.ufrgs.br/tex/fis142/mod01/m_s02.html [13/03/2004 16:18:17]

1.4 LEI DE GAUSS & LEI DE COULOMB

Capitulo 1 - A LEI DE COULOMBFORA ELETROSTTICANuma abordagem bastante geral, podemos dizer que dois corpos eletrizados interagem atravs da atrao gravitacional e da interao eletromagntica. Esta abordagem pode ser simplificada desprezando-se a atrao gravitacional frente interao eletromagntica. Na maioria dos casos tratados aqui essa uma boa aproximao. Podemos fazer outra simplificao, considerando apenas as cargas estacionrias. Eletrosttica esta rea do eletromagnetismo que aborda interaes entre cargas estacionrias ou quase estacionrias. Coulomb descobriu, experimentalmente, que a fora entre cargas q1 e q2 dada por: (1.1)

onde

=8.99x109 Nm2/C2 uma constante que tem

essa forma para atender necessidades de ajustes dimensionais e para simplificar as equaes de Maxwell. 0=8.85x10-12 C2/Nm2, uma constante muito importante no eletromagnetismo, denominada permissividade eltrica no vcuo.+e+ +e-e-

No aplicativo acima, v-se duas cargas eltricas.


1.4 LEI DE GAUSS & LEI DE COULOMB

1) Altere os sinais das cargas e observe os sentidos das foras de interao eletrosttica. 2) Clique sobre uma carga e veja, na barra amarela que fica na parte de baixo da moldura, o valor das coordenadas e da fora. 3) Fixe uma das cargas, e movimente a outra ao longo do eixo dos x's. Faa o grfico de F versus a distncia entre as cargas. Use pelo menos 10 pontos para fazer grfico. 4) Voc consegue explicar porqu foi sugerido que a carga se movimentasse ao longo dos eixo dos x's?


3.4 EXEMPLO 1.1

Capitulo 1 - A LEI DE COULOMBEXEMPLO 1.1Duas cargas positivas puntiformes, Q1 e Q2, so colocadas no eixo dos y, nos pontos y=+a e y=-a. Calcule a fora dessas duas cargas sobre uma terceira carga, q, colocada no eixo dos x. Vamos tomar a primeira providncia, vlida em quase todos os problemas de fsica: fazer um desenho que represente o enunciado. A figura 1.2 a expresso grfica do enunciado acima.

Pelo princpio da superposio,

.

Tendo em conta as posies das cargas, conforme figura acima, e que Q1=Q2=Q=q, tem-se F1=F2=kq2/r2. Por simetria chega-se concluso que a fora resultante sobre a terceira carga tem a direo do eixo x. Portanto, ohttp://www.if.ufrgs.br/tex/fis142/mod01/m_s04.html (1 de 2) [13/03/2004 16:18:24]

3.4 EXEMPLO 1.1

mdulo da fora resultante ser

Mostre que a fora resultante mxima no ponto Substituindo o valor negativo de x na expresso

. , obtm-

se um resultado positivo, em aparente contradio com os apontamentos ao lado. Tente descobrir onde est o equvoco.


1.6 Exercicios

Capitulo 1 - A LEI DE COULOMBExercicios.Pergunta 1q

1.1 Duas partculas igualmente carregadas, com um afastamento de 3x10-3 m entre elas, so largadas a partir do repouso. As partculas tm massas iguais a 7,0x10-7 kg e 5,4x10-7 kg, e a acelerao inicial da primeira partcula de 700 m/s2. Quais so: (a) a acelerao da segunda partcula? (b) O mdulo da carga comum? R.: 900 m/s2; 7x10-10 C.

Pergunta 2q

1.2 Considerando, na figura 1.3, q=2x10-6 C e a=10 cm, determine as componentes horizontais e verticais da fora resultante que atua na carga q (canto superior direito). As cargas esto em repouso absoluto. R.: 1,94kq2/a2; 0,06kq2/a2.

Figura 1.3http://www.if.ufrgs.br/tex/fis142/mod01/m_ex.html (1 de 3) [13/03/2004 16:18:30]

1.6 Exercicios

Pergunta 3q

1.3 Duas cargas pontuais livres, +q e +9q, esto afastadas por uma distncia d. Uma terceira carga colocada de tal modo que todo o sistema fica em equilbrio. (a) Determine a posio, o mdulo e o sinal da terceira carga. (b) Mostre que o equilbrio instvel. R.: Carga 9q/16, colocada entre as cargas +q e +9q, a uma distncia d/4 a partir da carga +q.

Pergunta 4q

1.4 Cargas iguais a +Q so colocadas nos vrtices de um tringulo equiltero de lado L. Determine a posio, o mdulo e o sinal de uma carga colocada no interior do tringulo, de modo que o sistema fique em equilbrio. R.: Carga

colocada na bissetriz, a uma distncia

a partir do vrtice.

Pergunta 5q

1.5 Uma carga Q igual a 2x10-19 C dividida em duas, (Q-q) e q, de modo que a repulso coulombiana seja mxima. Calcule a distncia que uma deve ficar da outra, para que esta fora seja igual 9x10-9 N. R.: 1

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1.6 Exercicios

Pergunta 6q

1.6 Duas cargas pontuais idnticas, de massa m e carga q, esto suspensas por fios no condutores de comprimento L, conforme ilustra a figura 1.4. Considerando o ngulo to pequeno de modo que seja vlida a aproximao , mostre que

Figura 1.4

Pergunta 7q

1.7 (a) Quantos eltrons devero ser removidos de uma pequena esfera, para deix-la com carga igual a +1,6x10-9 C? (b) Supondo que a esfera seja de cobre, e tenha massa igual a 3,11 g, calcule a frao dos eltrons totais da esfera que corresponde ao valor encontrado em (a). R.: 1010 eltrons; 1/1014.

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2.2 Ao a Distancia

Capitulo 2 - O CAMPO ELTRICOAo a DistanciaA fora coulombiana, assim como a fora gravitacional, so interaes distncia, um conceito mal compreendido, desde Newton at meados do sculo passado, quando Faraday introduziu a idia de campo. De acordo com o conceito de campo, a interao entre duas cargas, Q1 e Q2, ocorre atravs da ao do campo de uma delas sobre a outra. Operacionalmente, o campo assim definido

(2.1) onde a carga de prova, q0, to pequena quanto possvel. Isto , para se conhecer o valor do campo eltrico em determinado ponto, basta colocar uma carga de prova naquele ponto e dividir a fora medida pelo valor da carga. Apresenta-se nesta simulao, a configurao de campo eltrico criado por uma certa distribuio de carga. Uma carga de prova (vermelha) pode ser usada para se determinar o valor de E em qualquer ponto no interior da moldura. Coloque o cursor sobre a carga e veja o valor de E. O valor positivo, logo, a carga lquida na distribuio positiva. Tente colocar a carga de prova em vrios pontos com y=0 (aproximadamente igual a zero) e diferentes valores de x. Use uma dessas medidas e determine o valor da carga lquida da distribuio. Faa um grfico de E versus x. Compare este grfico "experimental" com um terico, obtido com o uso da eq.2.1.

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1.2 LINHAS DE FORA

Capitulo 2- O CAMPO ELTRICOLINHAS DE FORACom a introduo do conceito de campo, logo surgiu a dvida sobre como ele se apresentava no espao. Faraday props o conceito de linhas de fora. Existe uma bem definida relao entre campo e linhas de fora, de modo que conhecendo-se um, determina-se o outro.r

Em cada ponto do espao, a direo do campo determinada pela tangente linha de fora. Em cada ponto do espao, o valor do campo determinado pelo nmero de linhas por unidade de rea transversal. Quanto maior a densidade de linhas de campo, maior a intensidade do campo.

r

Uma forma bastante simples para visualizar linhas de campo, no caso do campo magntico: (1) colocar um m sob uma cartolina; (2) espalhar limalha de ferro sobre a cartolina. No aplicativo ao lado, so visualizadas as linhas de campo de quatro esferas carregadas. As esferas podem ser colocadas em qualquer ponto do espao definido pela moldura; basta colocar o apontador do mouse sobre a carga e arrast-la para o ponto desejado. Coloque as esferas em diferentes posies, e determine o sinal da carga de cada uma. Ordene as esferas de acordo com o mdulo das suas cargas. Se tiver dvida, entre no teleduc e tente tir-la com o professor ou com algum colega.http://www.if.ufrgs.br/tex/fis142/mod02/m_s02.html (1 de 2) [13/03/2004 16:18:34]

1.2 LINHAS DE FORA

No aplicativo ao lado, v-se duas cargas, e as linhas de campo (outra denominao tambm usada para linhas de fora) da configurao. A carga esquerda positiva e tem valor fixo. A carga direita pode ser positiva ou negativa, e tem seu valor ajustado atravs da barra de controle. Quando o cursor da barra de controle est na extremidade direita, a carga mxima, e quando est na extremidade esquerda a carga prxima de zero. Movimente o cursor, de uma extremidade outra, e tente descrever o que acontece com as linhas de campo. Para se introduzir o conceito de campo eltrico no incio deste captulo, utilizamos uma carga de prova, "to pequena quanto possvel". Use o experimento que voc acabou de fazer, e tente justificar por qu a carga de prova tem que ser "to pequena quanto possvel". DICA: a carga de prova serve para a medida do campo eltrico da outra carga. Isto significa que ela serve para se avaliar as linhas de campo da outra carga.


2.4 CAMPO DE UM DIPOLO ELTRICO

Capitulo 2 - O CAMPO ELTRICOCAMPO DE UM DIPOLO ELTRICODada uma carga puntiforme, q, e uma carga de prova, q0, a uma distncia r da primeira, tem-se

(2.2)

Portanto, pela definio de campo, eq. (2.1), tem-se o campo de uma carga puntiforme

(2.3) Dipolo eltrico uma configurao muito importante para o tema que estamos tratando. Consiste de um par de cargas de mesmo valor e sinais contrrios, separadas por uma distncia d.

Figura 2.1http://www.if.ufrgs.br/tex/fis142/mod02/m_s03.html (1 de 3) [13/03/2004 16:18:40]


Pelo princpio da superposio,

Use a eq. (2.3) e mostre que o campo do dipolo, num ponto da sua mediatriz, xd, dado por

(2.4), onde p=qd o momento de dipolo eltrico do dipolo. Teta = 0 Ey = +1 E(- = abaixo, +=acima) Q (verde = "+" vermelho = "-") = 1 CAtualizar valores

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Esta simulao permite analisar o efeito de um campo eltrico uniforme, representado pelas linhas de fora verticais (verdes), sobre um dipolo eltrico. Os vetores azuis sobre cada carga representam as foras sobre elas. Vrios parmetros podem ser alterados pelo usurio. O campo eltrico sempre na direo y, mas pode ter o sentido + ou , alm disso, seu mdulo pode assumir qualquer valor. Teta o ngulo entre a mediatriz do dipolo e a direo do campo eltrico. A carga verde positiva, e a vermelha, negativa. Ambas tm o mesmo valor, como deve ser no caso de um dipolo. A carga pode assumir qualquer valor. Inicialmente, coloque teta=0, E=+1 e Q=1 C. Tecle no boto "iniciar" e observe o movimento do dipolo. Tente explicar o movimento. Para facilitar a tarefa, faa o seguinte: Clique no boto "pausa" quando o dipolo estiver em diferentes posies; analise as foras sobre as cargas, e leve em contahttp://www.if.ufrgs.br/tex/fis142/mod02/m_s03.html (2 de 3) [13/03/2004 16:18:40]


a energia cintica adquirida por cada carga. Examine o movimento do dipolo, passo a passo, clicando nos botes "1 passo>>" e "

Apostila de Fisica EAD - Eletricidade, Magnetismo e Física Moderna

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