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CPHY 122
Class Notes 13
Instructor: H. L. Neal
1 Faradayís Law
Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be îinducedîin the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic Öeld strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic Öeld, rotating the coil relative to the magnet, etc.
B
d A
d s
S
Created using UNREGISTERED Top Draw 3.10 Nov 14,'106 7:23:53 PM
Faradayís law is a fundamental relationship which comes from one of Maxwellís four equa- tions: (^) I
C
E ds =
d dt
B ;
where
B =
I
S
B dA;
E =
d dt
B :
The quantity E is called the electromotive force (emf). Faradayís law is a succinct summary of the ways a voltage (or emf) may be generated by a changing magnetic environment. The induced emf is equal to the negative of the rate of change of magnetic áux. It involves the interaction of charge with magnetic Öeld.
2 Lenzís Law
When an emf is generated by a change in magnetic áux according to Faradayís Law, the polarity of the induced emf is such that it produces a current whose magnetic Öeld opposes the change which produces it. The induced magnetic Öeld inside any loop of wire always acts to keep the magnetic áux in the loop constant. In the examples below, if the B Öeld is increasing, the induced Öeld acts in opposition to it. If it is decreasing, the induced Öeld acts in the direction of the applied Öeld to try to keep it constant.
3 Eddy Currents
An eddy current is caused by a moving magnetic Öeld intersecting a conductor or vice-versa. The relative motion causes a circulating áow of electrons, or current, within the conductor. These circulating eddies of current create electromagnets with magnetic Öelds that oppose the change in the external magnetic Öeld (see Lenzís law above). The stronger the magnetic Öeld, or greater the electrical conductivity of the conductor, the greater the currents developed and the greater the opposing force.
4 Maxwellís Equations
I began this course with Maxwellís Equations: I E dA = Q=" 0 (Gaussílaw for E); (1) I B ds = 0 I + 0 " 0
dE dt
(Ampereís Law); (2) I B dA = 0 Gaussílaw for B); (3) I E ds =
dB dt
(Faradayís Law), (4)
