PhysicsLAB AP Free Response Question
1999 C1 E&M

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An isolated conducting sphere of radius a = 0.20 m is at a potential of -2,000 V.
 (a) Determine the charge Q on the sphere.

The charge is then concentrically surrounded by two uncharged conducting hemispheres of inner radius b = 0.40 m and outer radius c = 0.50 m, which are joined together as shown above, forming a spherical capacitor. A wire is connected from the outer sphere to ground, then removed.
(b) Determine the magnitude of the electric field in the following regions as a function of distance r from the center of the inner sphere.
 i. r < a

 ii. a < r < b

 iii. b < r < c

 iv. r > c

 (c) Determine the magnitude of the potential difference between the sphere and the conducting shell.

 (d) Determine the capacitance of the spherical capacitor.

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