Review 1

1. Review 1

2. Topics • Electric field, dielectrics and conductors • Problem 21.54 • Problem 22.39 • Problem 22.70 • Problem 23.64 • Problem 23.63

3. Electric field, dielectrics & conductors • Electric field • By definition, it points in the direction of motion of a positive point charge • Dielectrics • Molecules are polarized by an external electric field • Conductors • In equilibrium, E = 0 within conductor

4. Problem 21.54 An infinitely long rod of radius R carries a uniform volume charge density r. Show that the electric field is E = r R2/(2e0 r) r > R E = r r/(2e0) r < R

5. R r …21.54 Gauss’s law is always true. However, because this problem has cylindrical symmetry, the law can be used to find the electric field within and outside the rod by using concentric Gaussian surfaces

6. Problem 22.39 Electrons in a TV tube are accelerated from rest across a potential difference of 25 kV. Compute the speed with which the electrons hit the TV screen. me = 9.1 x 10-31 kg |e| = 1.6 x 10-19 C Hint: conservation of energy

7. Problem 22.70 A conducting sphere of radius R1 carries a charge Q1. It is surrounded by concentric spherical shell of radius R2 carrying charge Q2. Compute the potential at the sphere’s surface, choosing the potential at infinity to be zero.

8. … 22.70 There are two ways to approach this problem: • Compute the potential for the sphere and the shell separately and add the potentials. Remember: the potential is always with respect to some reference value (e.g., zero at infinity). • Compute the potential at the sphere’s surface directly from

9. Problem 23.64 A sphere radius R carries a charge Q spread uniformly over its surface. Show that the energy stored in its electric field is U = k Q2/2R

10. … 23.64 This can be done in different ways: e.g., given the energy density u = e0E2/2, write dU = udv, where dv = 4pr2dr is a thin shell of radius r and thickness dr. Then sum dU. Note:

11. Problem 23.63 A sphere radius R carries a charge Q spread uniformly through its volume. Show that the energy required to assemble the charge is U = 3k Q2/5R while the energy stored within the sphere is U = kQ2/10R

12. Problem 23.63 A sphere radius R carries a charge Q spread uniformly through its volume. Show that the energy required to assemble the charge is U = 3k Q2/5R while the energy stored within the sphere is U = kQ2/10R

13. … 23.63 The total potential energy of the charge is given where and putting together the pieces we get Note: this is the energy within the sphere as well as outside