Resource Lesson
A Special Case of Induction
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We are going to investigate how you would calculate the induced emf in a rectangular wire loop that lies parallel to a current-carrying wire having a variable current.
Experience tells us that we should use Ampere's Law to calculate the strength of the magnetic field passing through the wire. However, this field is not uniform, but varies inversely as the perpendicular distance from the wire.
Next, we need to calculate the flux passing through the loop, by referencing the equation
Finally, to calculate the induced emf, we would reference Faraday's Law
Let's begin by developing an expression for the flux passing through the loop. since the magnetic field is not uniform throughout the area, we need to build areas through which it is uniform and add these areas up to determine the total flux.
In the diagram, we see a strip that has an area of A = x(dy). If
dy
is small, the magnetic field will be uniform in this smaller area. Its flux contribution,
would be
Now all we need to do is add up all of these contributions to calculate the total flux through the loop. To do this we will set up an integral with limits from
a
to
a+y
.
Our next step will be to develop an expression for the induced emf using Faraday's Law.
Related Documents
Lab:
Labs -
Magnetic Field in a Solenoid
Labs -
RC Time Constants
Labs -
Telegraph Project
Resource Lesson:
RL -
A Comparison of RC and RL Circuits
RL -
A Guide to Biot-Savart Law
RL -
Dielectrics: Beyond the Fundamentals
RL -
Eddy Currents plus a Lab Simulation
RL -
Electric Field Strength vs Electric Potential
RL -
Electricity and Magnetism Background
RL -
Generators, Motors, Transformers
RL -
Induced Electric Fields
RL -
Induced EMF
RL -
Inductors
RL -
LC Circuit
RL -
Magnetic Field Along the Axis of a Current Loop
RL -
Maxwell's Equations
RL -
Motional EMF
RL -
RL Circuits
RL -
Spherical, Parallel Plate, and Cylindrical Capacitors
RL -
Torque on a Current-Carrying Loop
Review:
REV -
Drill: Induction
Worksheet:
CP -
Induction
CP -
Power Transmission
CP -
Transformers
NT -
Induction Coils
WS -
Induced emf
WS -
Practice with Induced Currents (Changing Areas)
WS -
Practice with Induced Currents (Constant Area)
TB -
Electric Field Strength vs Electric Potential
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