A metallic and straight thin wire (length 2a) rotates with a frequency f in a pl
ID: 1259590 • Letter: A
Question
A metallic and straight thin wire (length 2a) rotates with a frequency f in a plane perpendicular to a uniform field B.
a. Using Faraday's law, ? = d(B)/dt = -d{B.dS}/ dt develope using demensional analysis an sexpression in terms of a, f, B for the induced emf ? between the center of the wire and one end of the wire (which is at a distance a from the center)
b. Let B= 0.1 mT, a = 0.1 m, and f= 1 Hz.
Find the induced voltage difference between the two opposing ends of the rotating metallic wire. You can use your eqn from a)
Explanation / Answer
Note that
EMF = d(B dot dS)/dt
Thus, it has units of
[EMF] = [T][m^2][s^-1]
Thus, we must be able to produce this unit from a, f, and B.
[T] gets B
m^2 gets a^2
s^-1 gets gets f.
Thus, we can do that by using
EMF = B f a^2 [ANSWER]
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Using our formula,
EMF = 1.0*10^-6 V [ANSWER]