AP Free Response Question
2010 C3 E&M
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The long straight wire illustrated above carries a current I to the right. The current varies with time t according to the equation
, where I
_{0}
and K are positive constants and I remains positive throughout the time period of interest. The bottom of a rectangular loop of wire of width
b
and height
a
is located a distance
d
above the long wire, with the long wire in the plane of the loop as shown. A lightbulb with resistance
R
is connected in the loop. Express all algebraic answers in terms of the given quantities and fundamental constants.
(a) Indicate the direction of the current in the loop. Justify your answer.
(b) Indicate whether the lightbulb gets brighter, gets dimmer, or stays the same brightness over the time period of interest. Justify your answer.
(c) Determine the magnetic field at t = 0 due to the current in the long wire at distance
r
from the long wire.
(d) Derive an expression for the magnetic flux through the loop as a function of time.
(e) Derive an expression for the power dissipated by the lightbulb.
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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Lab:
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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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Telegraph Project
Resource Lesson:
RL -
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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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
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Power Transmission
CP -
Transformers
NT -
Bar Magnets
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Induction Coils
NT -
Magnetic Forces
NT -
Meters and Motors
WS -
Induced emf
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Magnetic Forces on Current-Carrying Wires
WS -
Magnetic Forces on Moving Charges
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Practice with Ampere's Law
WS -
Practice with Induced Currents (Changing Areas)
WS -
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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