PhysicsLAB AP Free Response Question
2008 C1 E&M

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A metal sphere of radius a contains a charge +Q and is surrounded by an uncharged, concentric, metallic shell of inner radius b and outer radius c, as shown above. Express all algebraic answers in terms of the given quantities and fundamental constants.
(a) Determine the induced charge on each of the following and explain your reasoning in each case.
 i. The inner surface of the metallic shell

 ii. The outer surface of the metallic shell

(b) Determine expressions for the magnitude of the electric field E as a function of r, the distance from the center of the inner sphere, in each of the following regions.
 i. r < a

 ii. a < r < b

 iii. b < r < c

 iv. c < r

(c) On the axes below, sketch a graph of E as a function of r.

 (d) An electron of mass me carrying a charge -e is released from rest at a very large distance from the spheres. Derive an expression for the speed of the particle at a distance 10c from the center of the spheres.

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