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.
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
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
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
resistance in parallel
resistance in series
resistivity
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