2. (a) Remember, an ampere is a coulomb per second of charge flow. Ampere hours then = coulomb hours per second. Justify time units and you have the answer.(3.0 x 105C) (b) Change in potential energy = charge times change in potential (3.6 x 106J)
4. sketch
8. (a) Electric field = force/charge (2.4 x 104 N/C) (b) potential difference = E (change in position) (2900 V)
9. Use expression for electric field for sheet of charge (eqn 25-15). Equipotential surfaces will be parallel to sheet. If E is expressed in volts/meter, delta x = (delta V)/E
16. (a) For point charge, equipotential surfaces are concentric spheres. Find radius from equation 26-19. ( 4.5m) (b) Equipotential surfaces will be equally spaced if V and r have a linear relationship; do they?
32. Write coordinates for points where circle crosses x axis. Point A (on left side) will have coordinate -(R + xc) and point B (on right side) will have coordinate R + (- xc) or R - xc. Let distance from charge q2 to origin be x2. Now, using eqn 26-20, write an expression for the potential at points A and B, set them equal to 0. You will have two eqns and two unknowns; use the 1st eqn and solve for one of the variables in terms of the other. Substitute this expression into the 2nd eqn and find the value for the variable. Now substitute this value into the 1st eqn to find the other unknown. If you use the actual coordinates, be careful with signs. It might be easier to simply use the actual distances of each charge from the points and sort out the coordinates later (potential is a scalar). (a: 8.1 nm) (b: -4.8 nm) (c) Set up eqns for potential at 5V. By inspection, we see that a non-zero potential greatly complicates the eqns.
60. Work equals change in potential energy; sum of effects from each stationary charge
67. Conservation of energy: kinetic converts to electric potential at minimum distance. (a) proton of charge e and Pb nucleus of charge 82 e (25 fm) (b) alpha of charge 2 e (50 fm)
74. sketch; remember shell theorem for E, V. Refer to fig 26-19: graphs are not the same outside the sphere.
36. Use eqn 26-28; use L/2 and symmetry
43. Remember E is the negative rate of change of V with respect to x
45. Take derivative of V with respect to z .
48. (a) Use eqn 26-25. Express dq in terms of charge density and R. Express r in terms of R and z. Integrate over charge distribution (circle) to get results. (b) Take derivative with respect to z.