Homework Assignment 12
Due Nov. 14, 1997

1. Problem 4.23 from the text.

2. Problem 4.25 from the text.

3. Problem 4.26 from the text.

4. Problem 4.27 from the text.

5. Problem 4.28 from the text.

6. A spherical capacitor consists of a solid metal sphere (r = 0.01 m) surrounded by a concentric metal sphere (inner radius = 0.02 m, outer radius = 0.021 m). Calculate the capacitance of the spherical capacitor if the medium between the conductors (the metal sphere and the metal shell) is free space.

7. In a very simplistic way, and helicopter can be modeled as a sphere with a diameter about the size of the chopper. Consider a large helicopter -- it could be modeled as a sphere with a diameter of, say, about 10 meters.

   1. What would be its capacitance -- i.e., what is the capacitance of a metal sphere with a 5 m radius?

   2. The earth's electric field is about 100 V/m. What is the potential of a helicopter hovering at an altitude of 30 meters?

   3. Using the results of (a) and (b), what charge is on a helicopter hovering at 30 m?

8. Consider a charged capacitor with a dielectric slab partially inserted, as shown below. Find the force on the slab. (Hint: Treat this as two capacitors: C₁ is the capacitance of the part with the dielectric already inserted, and C₂ is the capacitance of the part without the dielectric. Find: