Volume B: Electricity, Magnetism, and Optics
- Page ID
- 6219
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- B1: Charge & Coulomb's Law
- Charge is a property of matter. There are two kinds of charge, positive “+” and negative “-”. An object can have positive charge, negative charge, or no charge at all. A particle which has charge causes a force-per-charge-of-would-be-victim vector to exist at each point in the region of space around itself.
- B2: The Electric Field - Description and Effect
- An electric field is an invisible entity which exists in the region around a charged particle. It is caused to exist by the charged particle. The effect of an electric field is to exert a force on any charged particle (other than the charged particle causing the electric field to exist) that finds itself at a point in space at which the electric field exists. The electric field at an empty point in space is the force-per-charge-of-would-be-victim at that empty point in space.
- B3: The Electric Field Due to one or more Point Charges
- A charged particle (a.k.a. a point charge, a.k.a. a source charge) causes an electric field to exist in the region of space around itself. This is Coulomb’s Law for the Electric Field in conceptual form.
- B4: Conductors and the Electric Field
- An ideal conductor is chock full of charged particles that are perfectly free to move around within the conductor. Like all macroscopic samples of material, an ideal conductor consists of a huge amount of positive charge, and, when neutral, the same amount of negative charge. When not neutral, there is a tiny fractional imbalance one way or the other. In an ideal conductor, some appreciable fraction of the charge is completely free to move around within the conducting material.
- B5: Work Done by the Electric Field and the Electric Potential
- When a charged particle moves from one position in an electric field to another position in that same electric field, the electric field does work on the particle.
- B6: The Electric Potential Due to One or More Point Charges
- The electric potential due to a point charge is given by
- B7: Equipotential Surfaces, Conductors, and Voltage
- Consider a region of space in which there exists an electric field. Focus your attention on a specific point in that electric field, call it point A.
- B8: Capacitors, Dielectrics, and Energy in Capacitors
- Capacitance is a characteristic of a conducting object. Capacitance is also a characteristic of a pair of conducting objects.
- 9B: Electric Current, EMF, and Ohm's Law
- We now begin our study of electric circuits. A circuit is a closed conducting path through which charge flows. In circuits, charge goes around in loops.
- B10: Resistors in Series and Parallel; Measuring I & V
- The analysis of a circuit involves the determination of the voltage across, and the current through, circuit elements in that circuit.
- B11: Resistivity and Power
- For resistors that conform to Ohm’s Law, the resistance depends on the nature of the material of which the resistor is made and on the size and shape of the resistor. Energy is transformed from electric potential energy into thermal energy when a voltage is applied to the resistor. The electric field exerts a force on the charge carriers inside the seat of EMF in the direction opposite to the direction in which the charge carriers are going.
- B12: Kirchhoff’s Rules, Terminal Voltage
- There are two circuit-analysis laws that are so simple that you may consider them “statements of the obvious” and yet so powerful as to facilitate the analysis of circuits of great complexity known as Kirchhoff’s Laws. The first one, known as “Kirchhoff’s Voltage Law” or “The Loop Rule” states that, starting on a conductor, if you drag the tip of your finger around any loop in the circuit back to the original conductor, the sum of the voltage changes experienced by your fingertip will be zero.
- B13: RC Circuit
- Suppose you connect a capacitor across a battery, and wait until the capacitor is charged to the extent that the voltage across the capacitor is equal to the EMF Vo of the battery. Further suppose that you remove the capacitor from the battery.
- B14: Capacitors in Series & Parallel
- The method of ever-simpler circuits that we used for circuits with more than one resistor can also be used for circuits having more than one capacitor.
- B15: Magnetic Field Introduction - Effects
- We now begin our study of magnetism, and, analogous to the way in which we began our study of electricity, we start by discussing the effect of a given magnetic field without first explaining how such a magnetic field might be caused to exist.
- B16: Magnetic Field - More Effects
- The electric field and the magnetic field are not the same thing. An electric dipole with positive charge on one end and negative charge on the other is not the same thing as a magnetic dipole having a north and a south pole.
- B17: Magnetic Field: Causes
- This chapter is about magnetism but let’s think back to our introduction to charge for a moment. We talked about the electric field before saying much about what caused it.
- B18: Faraday's Law and Lenz's Law
- Do you remember Archimedes’s Principle? We were able to say something simple, specific, and useful about a complicated phenomenon.
- B19: Induction, Transformers, and Generators
- In this chapter we provide examples chosen to further familiarize you with Faraday’s Law of Induction and Lenz’s Law.
- B20: Faraday’s Law and Maxwell’s Extension to Ampere’s Law
- Consider the case of a charged particle that is moving in the vicinity of a moving bar magnet as depicted in the following diagram
- B21: The Nature of Electromagnetic Waves
- When we left off talking about the following circuit:
- B22: Huygens’s Principle and 2-Slit Interference
- Consider a professor standing in front of the room holding one end of a piece of rope that extends, except for sag, horizontally away from her in what we’ll call the forward direction.
- B23: Single-Slit Diffraction
- Single-slit diffraction is another interference phenomenon. If, instead of creating a mask with two slits, we create a mask with one slit, and then illuminate it, we find, under certain conditions, that we again get a pattern of light and dark bands.
- B24: Thin Film Interference
- As the name and context imply, thin-film interference is another interference phenomenon involving light.
- B25: Polarization
- The polarization direction of light refers to the two directions or one of the two directions in which the electric field is oscillating. For the case of completely polarized light there are always two directions that could be called the polarization direction.
- B26: Geometric Optics, Reflection
- We now turn to a branch of optics referred to as geometric optics and also referred to as ray optics.
- B27: Refraction, Dispersion, Internal Reflection
- When we talked about thin film interference, we said that when light encounters a smooth interface between two transparent media, some of the light gets through, and some bounces off.
- B28: Thin Lenses - Ray Tracing
- A lens is a piece of transparent material whose surfaces have been shaped so that, when the lens is in another transparent material (call it medium 0), light traveling in medium 0, upon passing through the lens, is redirected to create an image of the light source.
- B29: Thin Lenses - Lens Equation, Optical Power
- From the thin lens ray-tracing methods developed in the last chapter, we can derive algebraic expressions relating quantities such as object distance, focal length, image distance, and magnification.
- B30: The Electric Field Due to a Continuous Distribution of Charge on a Line
- Recall that Coulomb’s Law for the Electric Field gives an expression for the electric field, at an empty point in space, due to a charged particle. You have had practice at finding the electric field at an empty point in space due to a single charged particle and due to several charged particles. In the latter case, you simply calculated the contribution to the electric field at the one empty point in space due to each charged particle, and then added the individual contributions.
- B31: The Electric Potential due to a Continuous Charge Distribution
- We have defined electric potential as electric potential-energy-per-charge. Potential energy was defined as the capacity, of an object to do work, possessed by the object because of its position in space.
- B32: Calculating the Electric Field from the Electric Potential
- The plan here is to develop a relation between the electric field and the corresponding electric potential that allows you to calculate the electric field from the electric potential.
- B33: Gauss’s Law
- Gauss’s Law states that the number of electric field lines poking outward through an imaginary closed surface is proportional to the charge enclosed by the surface. A closed surface is one that divides the universe up into two parts: inside the surface, and, outside the surface. To be closed, a surface has to encompass a volume of empty space. A surface in the shape of a flat sheet of paper would not be a closed surface. An imaginary closed surface is often referred to as a Gaussian surface.
- B34: Gauss’s Law Example
- We finished off the last chapter by using Gauss’s Law to find the electric field due to a point charge.
- B35: Gauss’s Law for the Magnetic Field and Ampere’s Law Revisited
- Remember Gauss’s Law for the electric field? It’s the one that, in conceptual terms, states that the number of electric field lines poking outward through a closed surface is proportional to the amount of electric charge inside the closed surface.
- B36: The Biot-Savart Law
- The Biot-Savart Law provides us with a way to find the magnetic field at an empty point in space, let’s call it point P, due to current in wire.
- B37: Maxwell’s Equations
- In this chapter, the plan is to summarize much of what we know about electricity and magnetism in a manner similar to the way in which James Clerk Maxwell summarized what was known about electricity and magnetism near the end of the nineteenth century. Maxwell not only organized and summarized what was known, but he added to the knowledge. From his work, we have a set of equations known as Maxwell’s Equations. His work culminated in the discovery that light is electromagnetic waves.
Thumbnail: Lightning over the outskirts of Oradea, Romania, during the August 17, 2005 thunderstorm which went on to cause major flash floods over southern Romania. (Public Domani; Nelumadau).