Question

Chapter 22, Problem 27

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 0.15 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* = 2.3 T if the induced emf
is to be zero? Use a minus sign if the area is to be shrunk.

Answer #1

According to the question;

As we know that;

The magnitude of the induced emf is the time rate of change in
flux, B dot A. For your case the dot product is just BA and the
induced voltage is

V = d(BA)/dt

Then,

(a)

The area is constant;

V = AdB/dt = (0.014)(0.15) = 0.002 volts

Then,

(b)

Both B & A change;

V = AdB/dt + BdA/dt

dA/dt such that V=0, when B=2.4 and,presumably, when A=.014,

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

= -(0.014/2.3)(0.15)

= -0.0009m^2/s

So,

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

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