AP Free Response Question
2008 C1 E&M
Printer Friendly Version
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
m
_{e}
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.
Topic Formulas
Description
Published Formula
Ampere's Law
Biot-Savat Law
capacitance
capacitance (dielectric)
capacitors in parallel
capacitors in series
Coulomb's Law
current density
elastic potential energy
electric current
electric field
electric field strength
electric potential energy
energy stored in a capacitor
energy stored in an inductor
Faraday's Law
force ona current-carrying wire
Gauss' Law
induced emf (inductor)
induced emf (magnetism)
Joule's Law
kinetic energy
magnetic field around a current-carrying wire
magnetic field of a solenoid
magnetic flux
magnetic force on a moving charge
motional emf
Ohm's Law
parallel-plate capacitor
potential and electric field strength
potential due to a collection of point charges
potential energy
power
power
resistance in parallel
resistance in series
resistivity
work
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