AP Free Response Question
2008 C3 E&M
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The circular loop of wire in Figure 1 above has a radius of
R
and carries a current
I
. Point
P
is a distance of
R
_{2}
above the center of the loop. Express algebraic answers to parts (a) and (b) in terms of
R
,
I
, and fundamental constants.
(a) i. State the direction of the magnetic field B
_{1}
at point P due to the current in the loop.
(a) ii. Calculate the magnitude of the magnetic field B
_{1}
at point P.
A second identical loop also carrying a current
I
is added at a distance of
R
above the first loop, as shown in Figure 2 above.
(b) Determine the magnitude of the net magnetic field B
_{net}
at point P.
A small square loop of wire in which each side has a length
s
is now placed at point P with its plane parallel to the plane of each loop, as shown in Figure 3 above. For parts (c) and (d), assume that the magnetic field between the two circular loops is uniform in the region of the square loop and has magnitude
B
_{net}
.
(c) In terms of
B
_{net}
and
s
, determine the magnetic flux through the square loop.
(d) The square loop is now rotated about an axis in its plane at an angular speed
ω
. In terms of
B
_{net}
,
s
, and
ω
, calculate the induced emf in the loop as a function of time
t
, assuming that the loop is horizontal at t = 0.
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 flux
magnetic force on a current-carrying wire
magnetic force on a moving charge
magnetic force on a moving charge
motional emf
Ohm's Law
potential due to a collection of point charges
resistance in parallel
resistance in series
resistivity
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Magnetic Field in a Solenoid
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Mass of an Electron
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RC Time Constants
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Resource Lesson:
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A Guide to Biot-Savart Law
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A Special Case of Induction
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Ampere's Law
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Dielectrics: Beyond the Fundamentals
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Eddy Currents plus a Lab Simulation
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Electric Field Strength vs Electric Potential
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Electricity and Magnetism Background
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Famous Experiments: Cathode Rays
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Generators, Motors, Transformers
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Induced Electric Fields
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Induced EMF
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Inductors
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Introduction to Magnetism
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LC Circuit
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Magnetic Field Along the Axis of a Current Loop
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Magnetic Forces on Particles (Part II)
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Magnetism: Current-Carrying Wires
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Maxwell's Equations
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Meters: Current-Carrying Coils
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Motional EMF
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RL Circuits
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Spherical, Parallel Plate, and Cylindrical Capacitors
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Torque on a Current-Carrying Loop
Review:
REV -
Drill: Induction
Worksheet:
APP -
Maggie
APP -
The Tree House
CP -
Induction
CP -
Magnetism
CP -
Power Transmission
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Transformers
NT -
Bar Magnets
NT -
Induction Coils
NT -
Magnetic Forces
NT -
Meters and Motors
WS -
Induced emf
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Magnetic Forces on Current-Carrying Wires
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Magnetic Forces on Moving Charges
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Practice with Ampere's Law
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Practice with Induced Currents (Changing Areas)
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Practice with Induced Currents (Constant Area)
TB -
36A: Magnets, Magnetic Fields, Particles
TB -
36B: Current Carrying Wires
TB -
Electric Field Strength vs Electric Potential
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Exercises on Current Carrying Wires
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