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29a. Electromagnetic Induction
Assignment is due at 2:00am on Wednesday, March 7, 2007
Credit for problems submitted late will decrease to 0% after the deadline has passed.
The wrong answer penalty is 2% per part. Multiple choice questions are penalized as described in the online help.
The unopened hint bonus is 2% per part.
You are allowed 4 attempts per answer.
Electromanetic Induction
Conceptual Induction
A loop of wire is initially held above a short solenoid. A constant counterclockwise (as viewed from above) current
passes through the coils of the solenoid. Suppose that the loop of wire is steadily
lowered, passing over the solenoid.
When asked for the direction of current thoughout this problem, suppose that you are viewing the wire loop from above, looking downward.
Part A
What is the direction of the induced current in the loop when the loop is above the solenoid, moving downward?
Part A.1
What is the direction of the magnetic field in the solenoid?
To solve Parts A, B, and C, you will need to use Lenz's law. The current in the solenoid generates a magnetic field. As the wire loop approaches the solenoid, the magnetic flux passing through the
loop (due to the solenoid's magnetic field) changes. A current will be induced in the loop, and the flux produced by this induced current must oppose the change in flux due to the solenoid's magnetic
field. What is the direction of the magnetic field that passes through the interior of the solenoid?
ANSWER:
up
down
Hint A.2
Faraday's law
You can think about this problem in terms of the Faraday's law. According to this law, the electromotive force (EMF)
that produces current in the loop is given by
, where
is the magnetic flux through the loop. Pay attention at the minus sign. This minus sign means that if the magnetic flux is increasing, then the EMF is such that it produces the current whose induced
magnetic field will be in the opposite direction to that of
, while if the magnetic flux is decreasing, then the induced field is in the direction of
.
ANSWER:
clockwise
counterclockwise
no current
Part B
What is the direction of the induced current when the loop is at the midpoint of the solenoid and still moving downward?
Hint B.1
Applying Lenz's law
As the loop approaches the solenoid from above, the number of magnetic field lines passing through the loop due to the magnetic field of the solenoid increases. (The number of magnetic field lines
passing through the loop represents the magnitude of the magnetic flux through the loop.) The number of field lines passing through the loop will continue to increase until the loop arrives at the
midpoint of the solenoid. Once the loop travels beyond the solenoid's midpoint, the number of field lines passing through the loop begins to decrease. Therefore, when the loop is exactly at the
midpoint of the solenoid, the number of field lines passing through the loop must be neither increasing nor decreasing. At the instant the wire loop is at the midpoint of the solenoid, there is no change
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 Spring '09
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 Magnetic Field, Faraday

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