AP Free Response Question
2003 C1 E&M
Printer Friendly Version
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
Related Documents
Lab:
Labs -
Aluminum Foil Parallel Plate Capacitors
Labs -
Electric Field Mapping
Labs -
Electric Field Mapping 2
Labs -
Magnetic Field in a Solenoid
Labs -
Mass of an Electron
Labs -
RC Time Constants
Resource Lesson:
RL -
A Comparison of RC and RL Circuits
RL -
A Guide to Biot-Savart Law
RL -
A Special Case of Induction
RL -
Capacitors and Dielectrics
RL -
Continuous Charge Distributions: Charged Rods and Rings
RL -
Continuous Charge Distributions: Electric Potential
RL -
Coulomb's Law: Beyond the Fundamentals
RL -
Coulomb's Law: Suspended Spheres
RL -
Derivation of Bohr's Model for the Hydrogen Spectrum
RL -
Dielectrics: Beyond the Fundamentals
RL -
Electric Field Strength vs Electric Potential
RL -
Electric Fields: Parallel Plates
RL -
Electric Fields: Point Charges
RL -
Electric Potential Energy: Point Charges
RL -
Electric Potential: Point Charges
RL -
Electrostatics Fundamentals
RL -
Famous Experiments: Millikan's Oil Drop
RL -
Gauss' Law
RL -
Inductors
RL -
LC Circuit
RL -
Magnetic Field Along the Axis of a Current Loop
RL -
Maxwell's Equations
RL -
Parallel Plate Capacitors
RL -
RL Circuits
RL -
Shells and Conductors
RL -
Spherical, Parallel Plate, and Cylindrical Capacitors
RL -
Torque on a Current-Carrying Loop
Review:
REV -
Drill: Electrostatics
REV -
Electrostatics Point Charges Review
Worksheet:
APP -
The Birthday Cake
APP -
The Electrostatic Induction
CP -
Coulomb's Law
CP -
Electric Potential
CP -
Electrostatics: Induction and Conduction
NT -
Electric Potential vs Electric Potential Energy
NT -
Electrostatic Attraction
NT -
Lightning
NT -
Photoelectric Effect
NT -
Potential
NT -
Van de Graaff
NT -
Water Stream
WS -
Capacitors - Connected/Disconnected Batteries
WS -
Charged Projectiles in Uniform Electric Fields
WS -
Combinations of Capacitors
WS -
Coulomb Force Extra Practice
WS -
Coulomb's Law: Some Practice with Proportions
WS -
Electric Field Drill: Point Charges
WS -
Electric Fields: Parallel Plates
WS -
Electric Potential Drill: Point Charges
WS -
Electrostatic Forces and Fields: Point Charges
WS -
Electrostatic Vocabulary
WS -
Induced emf
WS -
Parallel Reading - The Atom
WS -
Standard Model: Particles and Forces
TB -
Advanced Capacitors
TB -
Basic Capacitors
TB -
Electric Field Strength vs Electric Potential
CB-ETS
Copyright © 1970-2022
All rights reserved.
Used with
permission
Mainland High School
Daytona Beach, FL 32114