AND 23.8) ELECTRIC CHARGE AND ELECTRIC FIELDS

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1 Objectives for PH2640 FINAL EXAM: Yellow highlighted items represent the body of knowledge that is fair game for the final exam. Lined out items will not be on the final. Non-highlighted items have close overlap with a highlighted one, or could provide alternative means of solving problems. (I.e. symmetry and Coulomb s law not necessary, but could be a nice way to solve some problems.) OPTICS Ch. 20 p ; Ch. 21 p ; Ch (Wave Optics) 1) Given to you: wavelength dependence on n; relationship between frequency, speed, wavelength of light waves; phase reversal upon reflecting from higher-n materials; constructive/destructive interference requirement (Eq ); double-slit bright fringe location; diffraction grating fringe location; minima location for single slit & circular aperture; Michelson interferometer relationship 2) Know (not given): when small-angle approximation is appropriate 3) Determine any one of [frequency/wavelength/speed] of a light wave, given the other two properties; a) this could include properties when passing through a material with index of refraction n. 4) Know (not given): phase differences for constructive/destructive interference between waves; how to determine angles/conditions for constructive/destructive interference. 5) Given any of {diffraction grating/double slit/single slit/circular aperture}, determine the positions at which various wavelengths have intensity maxima/minima (don t worry about maxima for single slit or circular aperture) a) Either angular positions or locations on a screen 6) Given two paths in a thin, partially reflective film, determine whether one observes constructive or destructive interference. a) Calculate the thickness of this film in order to have a weak or strong reflection for a particular color 7) Determine the wavelength from the movement of a mirror in a Michelson interferometer; alternatively, determine the expected number of fringes from a movement of one of its mirrors. 8) Use the concept of single-slit/circular aperture diffraction to determine whether the wave or ray model of light is appropriate. Ch. 23: Ray Optics 1. Given to you: Snell s law, critical angle for total internal reflection; magnification; thin lens equation; lens maker s equation; minima location for circular aperture. 2. Know (not given): law of reflection; conditions required for total internal reflection; convention of angles for Snell s law; sign convention for converging/diverging focal lengths, radii of curvature, and real/virtual images; application of diffraction-limited spot size from Ch. 22 to lenses; the difference between real and virtual images; be able to give the definition of a focal point 3. Use the ray model of light to determine the size of a patch of light, including cases with reflection 4. Determine the direction of travel as a ray passes through several materials of given n; also determine n given the path. 5. Determine if a ray undergoes total internal reflection at an interface; also determine the angle of incidence required for total internal reflection 6. Describe/explain qualitatively, in terms of the propagation of light: why is the sky blue and the sunset red, why are leaves green, why does a prism give us a rainbow, etc. (i.e. Section 23.5) 7. Use the lens maker s equation to determine the focal length of a lens; alternatively, use the focal length to determine a curvature radius of a lens face, or the index of refraction of a lens material 8. Determine the focal length lens required for a desired magnification; also, the magnification resulting from a given lens 9. Locate the image of an object for a one- or two-lens system. a. Give whether image is upright or inverted; real or virtual; and magnification b. You may use ray tracing as a visual aid, but you will not be tested on this. 10. Use the diffraction limit to determine the angular resolution of a telescope, or the required size of a lens 11. SKIP: single-spherical-surface refraction (Eq , with R not approaching infinity) AND resolution (Ch. 23.8) ELECTRIC CHARGE AND ELECTRIC FIELDS Ch. 25: Electric charge, force, and field 1. Given to you: Coulomb s law, electric field from a point charge, k, epsilon-0, charge of an electron 2. Facts: know the basic element of charge is an electron; know the difference between insulators & conductors (with respect to the motion of charges in these objects); know (and use) the appropriate units in dealing with

2 electrostatics; know what dipoles are; know how charged/uncharged objects attract/repel/don t interact; know the definition of the electric field; know units of charge; interpret sketches of electric field lines. 3. Determine the number of extra (deficient) electrons on an object with a net charge. 4. Use Coulomb s Law to calculate the (up to 2-D) net force on a charge due to a collection of charges. 5. Use force balance, including gravity, in conjunction with Coulomb s Law to describe the equilibrium position of particles and objects. 6. Use the conservation of charge to describe how charge flows between charged objects that are connected, grounded, etc. 7. Use symmetry to help make calculations of Coulomb s Law simpler. 8. Describe, in terms a freshman in engineering could understand, what is meant by the electric field. What is it? 9. Find the net electric field at any point due to a collection of point charges. 10. Use the electric field model, in conjunction with force balance, including gravity, to describe the equilibrium position of particles and objects. Ch. 26: The Electric Field 1. Given to you: F=ma; electric field from dipole, infinite line of charge, infinite plane of charge, sphere of charge, and inside capacitor; constant acceleration equations. 2. Know (not given): definition of electric field; definition of charge density,; definition of capacitor; significance of charge in a capacitor; definition of dipole moment p. 3. Calculate the net electric field from a collection of point charges; use symmetry to simplify this. 4. Determine the electric field at a point from the charged standard objects given above (dipole, sheet, line, point, sphere), and from combinations of the objects. 5. Find the electric field at a given point from a continuous distribution of charge (straight line or circular arc); you will be asked to set up an integral with proper arguments and integration limits, but not to solve it. Guaranteed to be on the exam. 6. Use the electric field from standard objects (point, line, sphere, sheet, dipole) to find forces/accelerations on a charged particle. Apply this result to motion problems. 7. Determine the electric field in a capacitor from its charge. 8. Determine the force between a dipole and an ion, given dipole dimensions and charge, distance: see Example SKIP section 26.7 (dipole rotation), except for Example Ch. 27: Gauss Law 1. Given to you: Gauss Law, flux definition equation; external electric field near the surface of a charged conductor 2. Know: sign determination on flux through a (closed) surface; the distribution of charge in a conductor, including one with cavities 3. Determine the flux through any arbitrary closed surface, given a charge distribution and vice versa. 4. Given an electric field distribution, determine the flux through an object (i.e. a box, or a surface). Use this information to determine the net charge inside a closed surface. 5. Use symmetry to help determine the flux through any surface. 6. Use Gauss Law, in conjunction with the definition of electric flux, to calculate the electric field around symmetric charge distributions (cylindrical or spherical, conductors and insulators) 7. Determine the electric field at the surface of a conductor, given its charge (or charge density) 8. Use #6 in determining the electric field due to induced charges in a conductor (i.e. in a cavity). ELECTRIC CIRCUITS Ch. 28: Current & Conductivity 1. Given to you: relationship between current density and electric field; relationship between resistivity and conductivity; table of conductivities and resistivities; definition of current density; relation between electron current and drift speed; relation between electron current and electric field/mean collision time; definition of macroscopic current; expression for conductivity in terms of material properties. 2. Know: (not given) Junction current rule; direction of current flow vs. charge of carriers; properties of superconductors; units for the above; difference between electron current and macroscopic current; concepts relating current density, drift speed, current, electric field, and mean time between collisions in a conductor (i.e. number-free problems under what conditions do they increase/decrease/stay the same?) 3. Describe the microscopic flow of charge/electrons at various points in a conductor, and on either side of a junction. Typical speeds (order of magnitude)? 4. Describe, in terms of charges and electrons, what happens inside a battery. 5. Determine the drift speed of charge carriers from current (and geometry). 6. Determine the current density from current, geometry of conductor, and/or electric field.

3 7. Determine any one of {the electric field in a conductor, its current (electron current or charge current), physical properties (resistivity/conductivity), and geometry} from the other 3 parameters. Ch. 29: The Electric Potential 1. Given to you: Relationship between work & potential energy; expression for total mechanical energy; relationship between electric potential and potential energy; relationship between delta_v & E in a parallelplate capacitor; potential energy and electric potential from point charges (any number); electric potential from a disk of charge, and ring of charge; potential energy of a dipole 2. Know: (not given) units for the above; difference between electric potential & electric potential energy; potential of a charged sphere; definition of a conservative force; definition of equipotential surfaces; direction of voltage change along/across an E field line; know how to use energy conservation. 3. Given an array of point charges and/or charged spheres, (a) determine the electric potential at any point in space; (b) determine the energy of this array of charges. 4. Use conservation of energy with moving, charged particles to determine any one of {charges, velocities, positions} when given the other two and any of {electric field, surface charge density, change in electric potential, change in position}. 5. Determine the amount of energy involved in transferring charge across an electric potential, and use energy to relate back to changes in electrostatic potential (i.e. an electron slows; through what potential difference did it move). 6. Using energy conservation and potential energy, determine the energy required to rearrange a distribution of charges. 7. Given any of the {charge, voltage, electric field} of a conductor, determine the other quantities. 8. Determine the distance between equipotential surfaces surrounding an object(s), given a charge distribution and/or electric field. 9. SKIP: 29.3, dipole potential energy, and most of 29.7 (Continuous distribution of charge) Ch. 30: Potential and Field 1. Given to you: finding V from E; finding E from V;; definition of parallel-plate capacitance; current-voltageresistance relationship; definition of capacitance; energy stored in a capacitor; energy in an electric field 2. Know: (not given): how to combine capacitors in series and parallel (and definitions of series, parallel); geometrical relationship between E and equipotential surfaces; definition of equipotential surfaces; units of resistance, capacitance; properties of a conductor: electric field and electric potential 3. Determine the voltage drop (change in electric potential) when moving through an electric field, whether uniform E or not; also, find E given V(x). 4. Relate the energy supplied by a battery to the amount of charge it lifts from its negative terminal to its positive terminal. 5. Given any two of (current, voltage, resistance/geometry of resistor), determine the third quantity. 6. Given any two of the (charge, emf/voltage, capacitance) of a simple circuit with a capacitor, determine the third quantity. 7. Determine the energy stored in a capacitor; you may need to determine the capacitance/charge/electric potential from other information (i.e. #30.33) 8. Determine the charge and voltage across every capacitor in a multiple-capacitor circuit. 9. Understand conceptually/qualitatively the relationship between electric potential drop, electric field, electric field energy, and electric potential energy. Ch. 31: Fundamentals of Circuits 1. Given to you: Definition of resistance, Ohm s law, power supplied by a battery, power dissipated by a resistor, Kirchoff s loop & junction laws, expressions for series & parallel resistor combinations, charge & current in an RC circuit as a function of time. 2. Know: (not given): which expression is needed for series/parallel resistor combinations; sign conventions for voltage rises or drops; recognize, from a drawing or from a circuit diagram, series and parallel combinations of elements; significance of a kilowatt-hour, internal resistance, and the ground symbol in a circuit diagram; definition of the time constant of an RC circuit. 3. Using Ohm s law and Kirchoff s laws, solve simple circuits. SKIP section Solving a circuit means determining the current through each element, the voltage drop across each element, and the power dissipated/supplied by each element. Elements may be connected in series or in parallel. a. Determine the current/power supplied by a battery that supplies a network of series and/or parallel resistors. Note this is different from solving the circuit, above. 4. Solve single-loop circuits involving a battery s internal resistance. 5. Determine the time required for the charge or current in an RC circuit to reach a desired value. a. Be able to do this with series and/or parallel combinations of resistors, and of capacitors.

4 Ch. 32: The Magnetic Field 1. Given to you: Biot-Savart law for charge and current; Ampere s law in integral form; magnetic field from a coil at any point along its axis; magnetic field from a long straight wire; magnetic field from a dipole moment (on-axis); magnetic force on a moving charged particle; force on a current perpendicular to a magnetic field; torque on a loop of current in a magnetic field; magnetic field from a solenoid. 2. Know (not given): how to determine the direction of a vector cross-product; the right-hand rule for the relationship between current and magnetic field direction; what is a cyclotron frequency & how does one change it; units on magnetic field & some typical magnitudes found in engineering & nature; what is a solenoid & what s so special about it 3. Sketch magnetic field lines around a current-carrying wire and/or a permanent magnet. 4. Describe, in words, Know the significance of Ampere s Law. How is it similar to Gauss Law? 5. Use Ampere s Law to determine the magnetic field (1) at the surface of a conductor; (2) inside a currentcarrying wire region (i.e. Example 32.8) 6. Use the Biot-Savart law and superposition to find the magnetic field at any point in space caused by one or more moving charged particles. 7. Use superposition to find the net magnetic field due to a combination of current-carrying wires and moving charged objects. No integration set-ups (i.e. Ch derivations) 8. Calculate the magnetic field from a given magnetic dipole moment (or current and geometry) & vice versa! 9. Determine the magnetic field inside a solenoid given its physical dimensions. Describe a solenoid that will give a desired magnetic field. a. SKIP 32.6, except solenoids 10. Determine the magnetic force on a moving charged particle and/or on a current-carrying wire. You may need to first calculate B from surrounding objects. a. Circular motion of charged particles is included here: understand and apply the radius of curvature of a path. b. Use this relationship as applied to items such as rail guns, wires supported by B fields, etc 11. Determine the motion of a charged particle under the influence of both electric and magnetic fields (i.e. mass spectrometry, Hall voltage, electrolysis, electron beams). 12. From geometry and the direction of the current, determine the torque and/or net force on a current-carrying coil in an external magnetic field. 13. Describe the mechanisms of natural magnetism. Why are some materials magnetic and not others? What does it mean to be magnetized? Ch. 33: Electromagnetic Induction 1. Given to you: Equations: Faraday s law, magnetic flux across a surface, solenoid inductance, voltage across an inductor, energy stored in an inductor, magnetic energy density, LC oscillation frequency, definition of inductance 2. Know (not given): direction of induced electric field/emf using Lenz law; how to change the flux through a loop (3 ways); how to create an induced current; the mechanism behind eddy current braking 3. Know the definition of the motional emf and calculate its magnitude 4. Calculate the magnetic flux through a surface, a. Which may involve an integral; 5. Use the changing flux to determine the induced emf; a. this may involve taking a derivative b. Use the induced emf to determine such things as current in a wire, force on a wire, etc. 6. Determine the inductance of a solenoid; use the relationship between current and voltage in an inductor to determine such quantities as inductance, peak voltage, allowable rate of change of current 7. In a circuit consisting of inductors and capacitors, find the current, stored energy, and voltage across the inductor at any time after a switch is closed. Be able to determine the frequency of oscillation of an LC circuit; choose circuit elements to achieve a target frequency. 8. Describe, in your own words, how a transformer works. What are the primary, secondary coils? Calculate the voltage in the secondary, or the number of coil turns for a particular secondary voltage. 9. Determine the size of an inductor to store a given amount of energy; determine the amount of energy stored in a magnetic field in space. 10. SKIP Ch. 34: Electromagnetic Fields and Waves 1. Given to you: Gauss law for magnetism; relation between E & B magnitudes in an electromagnetic wave; Poynting vector definition; intensity in terms of electric field, source power; transmitted intensity of polarizing sheets; relation between wave speed, frequency, & wavelength; intensity vs. distance from source of power P; relative magnitudes of E and B in an electromagnetic wave

5 2. Know (not given): relative orientations of E and B in an electromagnetic wave; the speed of an electromagnetic wave emitted by an antenna; definition of polarization 3. Apply Gauss Law for magnetism to find the magnetic field through a portion of a closed surface (i.e. problem #1) 4. Determine the electric field (magnitude and direction) created by a magnetic field changing in time. 5. Determine the magnetic field (magnitude and direction) created by an electric field that changes in time. 6. Find the amplitude of the electric/magnetic fields in electromagnetic radiation, given its received intensity. Find the field amplitude after the radiation has propagated a given distance a. SKIP radiation pressure 7. Find the transmitted intensity (and, by extension, field strengths) for light (either polarized or unpolarized) transmitted through a series of polarizing sheets at various orientations.