Problems for the Week of Oct

Problems for the week of Oct. 16

50. A conducting spherical shell of inner radius a and outer radius b carries a net charge Q. A point charge q is placed at the center of this shell. Determine the surface charge density on (a) the inner surface of the shell and (b) the outer surface of the shell.

57. A solid, insulating sphere of radius a has a uniform charge density ρ and a total charge Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c, as shown in Figure P24.57. (a) Find the magnitude of the electric field in the regions r < a, a r < b, b < r < c, and r > c. (b) Determine the induced charge per unit area on the inner and outer surfaces of the hollow sphere.

Figure P24.57

3. (a) Calculate the speed of a proton that is accelerated from rest through a potential difference of 120 V. (b) Calculate the speed of an electron that is accelerated through the same potential difference.

13. An insulating rod having linear charge density λ = 40.0 μC/m and linear mass density μ = 0.100 kg/m is released from rest in a uniform electric field E = 100 V/m directed perpendicular to the rod (Fig. P25.13). (a) Determine the speed of the rod after it has traveled 2.00 m. (b) What If? How does your answer to part (a) change if the electric field is not perpendicular to the rod? Explain.

Figure P25.13

18. A charge +q is at the origin. A charge –2q is at x = 2.00 m on the x axis. For what finite value(s) of x is (a) the electric field zero? (b) the electric potential zero?

23. Show that the amount of work required to assemble four identical point charges of magnitude Q at the corners of a square of side s is 5.41keQ2/s.