AP Free Response Question
2003 C1 E&M
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A spherical cloud of charge radius
R
contains a total charge
+Q
with a non-uniform volume charge density that varies according to the equation
where
r
is the distance from the center of the cloud. Express all algebraic answers in terms of
Q
,
ρ
,
R
, and fundamental constants.
(a) Determine the following as a function of
r
for r > R.
i. The magnitude
E
of the electric field
ii. The electric potential
V
(b) A proton is placed at point P shown above and released. Describe its motion for a long time after its release.
(c) An electron of charge magnitude
e
is now placed at point P, which is a distance
r
from the center of the sphere, and released. Determine the kinetic energy of the electron as a function of
r
as it strikes the cloud.
(d) Derive an expression for ρ
_{o}
.
(e) Determine the magnitude
E
of the electric field as a function of
r
for r < R.
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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Lab:
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Aluminum Foil Parallel Plate Capacitors
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Electric Field Mapping 2
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Magnetic Field in a Solenoid
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Mass of an Electron
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RC Time Constants
Resource Lesson:
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A Comparison of RC and RL Circuits
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A Guide to Biot-Savart Law
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A Special Case of Induction
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Capacitors and Dielectrics
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Continuous Charge Distributions: Charged Rods and Rings
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Continuous Charge Distributions: Electric Potential
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Coulomb's Law: Beyond the Fundamentals
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Coulomb's Law: Suspended Spheres
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Derivation of Bohr's Model for the Hydrogen Spectrum
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Dielectrics: Beyond the Fundamentals
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Electric Field Strength vs Electric Potential
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Electric Fields: Parallel Plates
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Electric Fields: Point Charges
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Electric Potential Energy: Point Charges
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Electric Potential: Point Charges
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Electrostatics Fundamentals
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Famous Experiments: Millikan's Oil Drop
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Gauss' Law
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Inductors
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LC Circuit
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Magnetic Field Along the Axis of a Current Loop
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Maxwell's Equations
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Parallel Plate Capacitors
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RL Circuits
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Shells and Conductors
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Spherical, Parallel Plate, and Cylindrical Capacitors
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Torque on a Current-Carrying Loop
Review:
REV -
Drill: Electrostatics
REV -
Electrostatics Point Charges Review
Worksheet:
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The Birthday Cake
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The Electrostatic Induction
CP -
Coulomb's Law
CP -
Electric Potential
CP -
Electrostatics: Induction and Conduction
NT -
Electric Potential vs Electric Potential Energy
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Electrostatic Attraction
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Lightning
NT -
Photoelectric Effect
NT -
Potential
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Van de Graaff
NT -
Water Stream
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Capacitors - Connected/Disconnected Batteries
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Charged Projectiles in Uniform Electric Fields
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Combinations of Capacitors
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Coulomb Force Extra Practice
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Coulomb's Law: Some Practice with Proportions
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Electric Field Drill: Point Charges
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Electric Fields: Parallel Plates
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Electric Potential Drill: Point Charges
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Electrostatic Forces and Fields: Point Charges
WS -
Electrostatic Vocabulary
WS -
Induced emf
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Parallel Reading - The Atom
WS -
Standard Model: Particles and Forces
TB -
Advanced Capacitors
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Basic Capacitors
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Electric Field Strength vs Electric Potential
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