Download Chapter 31: Faraday`s Law

Faraday's Law
Study Guide for Chapter 31
Outline
1. Faraday's Law of Induction
Sometimes magnetic fields can create current in a wire. This process is known as induction, and
the resulting current is induced current.
This only happens when a wire moves through magnetic field lines. Specifically, current is
induced whenever
•
•
A wire moves through a magnetic field, or
A magnetic field moves (or changes) near a wire.
The induced emf in a loop of wire is given by the following equation:
Xœ
. FF
.>
(Faraday's EMF Law)
Here FF is the magnetic flux through the loop of wire.
Problems: 2, 3, 7, 13, 17
Answers: 2. !Þ) mA
2. Motional emf
This section derives a formula for the emf induced in a straight segment of wire moving through
a constant magnetic field:
X œ FP@
Here F is the magnetic field, P is the length of the segment, and @ is the velocity of the segment.
This formula only works for a straight wire, and it assumes that the magnetic field, the length of
the wire, and the velocity are all perpendicular.
Problems: 21, 22, 23
Answers: 22. " mÎs
3. Lenz's Law
A changing magnetic field induces current, but any current produces magnetic field:
Changing B
Ê
Induced Current
Ê
Extra B
Because of the negative sign in Faraday's law, the extra B opposes the original change in B. For
example:
• If you try to decrease B in the vicinity of a loop of wire, the induced current will reinforce the
existing magnetic field, opposing the decrease in B.
•
If you try to increase B in the vicinity of a loop of wire, the induced current will create a
magnetic field in the opposite direction, opposing the increase in B.
3. Induced emf and Electric Fields
In reality, a moving magnetic field actually creates an electric field, and this electric field is
responsible for the induced current. The induced electric field circles around the moving
magnetic field lines, according to the following law:
* any E † . s œ 
loop
. FF
.>
(Faraday's Law)
This law applies to any closed path that you can imagine. The integral is taken around the closed
path, and FF is the total magnetic flux through the middle of the path.
Problems: 33, 32
Answers: 32. (a) )Þ!" ‚ "!#" N counterclockwise (b) > œ "Þ$$ s
4. Generators and Motors
If you spin a loop of wire around inside a magnetic field, you get current that alternates back and
forth. This is called a generator, and it produces alternating current. The induced emf is
X œ EF = sin =>
where E is the area of the loop, F is the magnetic field, and = is the angular frequency of the
spinning. (That is, = œ #10 , where 0 is the frequency, or = œ #1ÎX , where X is the period.)
A generator operating in reverse is called a motor.
Problems: 35
5. Eddy Currents
A large metal object moving around in a magnetic field will experience eddy currents. These
generally oppose the motion of the object.