Question

A magnetic field is passing through a loop of wire whose area is
0.014 m^{2}. The direction of the magnetic field is
parallel to the normal to the loop, and the magnitude of the field
is increasing at the rate of 0.29 T/s. **(a)**
Determine the magnitude of the emf induced in the loop.
**(b)** Suppose the area of the loop can be enlarged
or shrunk. If the magnetic field is increasing as in part
**(a)**, at what rate (in m^2/s) should the area be
changed at the instant when *B* = 2.4 T if the induced emf
is to be zero? Use a minus sign if the area is to be shrunk.

Answer #1

V = d(BA)/dt

(a) the area is constant so;

V = AdB/dt = (.014)(.29) = .004 volts

(b) Both B & A change so;

V = AdB/dt + BdA/dt

You want to find dA/dt such that V=0, when B=2.4 and,presumably,
when A=.014:

dA/dt = - (A/B)dB/dt

= -(.014/2.4)(.29)

= -.0017 m^2/s

Since it is a negative rate the Area must be decreasing.

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