A loop of wire enclosing an area A is in a region with the magnetic field, perpe

Question

A loop of wire enclosing an area A is in a region with the magnetic field, perpendicular to the plane of the wire. The magnitude of this field is changing with time, B(t) = B0e-at, where a is a constant. (9 points)

a Find the induced emf in the loop as a function of time.
b After 5 seconds, the emf is a half of the initial emf, ?(t = 0). Find the value of a.
c If the shape of the loop is a square with the length of 10 cm and the initial emf, ?(t = 0) = 1.5 V, what it the magnitude of the magnetic field after 10 s?

Explanation / Answer

a)e = AB0 (e^-at)/a b) after 5 seconds it is half => e^(-a5) = 0.5 =>a =0.1386 c)1.5 = 100 *10^-4 *B0 /0.1386 => B0 =20.79 B after 10 seconds = B0 * e^(-a10) = 20.79/4 = 5.2

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