Question

A magnetic field is passing through a loop of wire whose area is 0.020 m2. 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 0.24 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 = 2.1 T if the induced emf is to be zero? Use a minus sign if the area is to be shrunk

Answer 1

Answer:

a) E = 0.0048 Volts

b)  dA/dt = - 0.002285 m²/s

Explanation:

Given:

Area, A = 0.020 m²

Rate of change of magnetic field, dB/dt = 0.24 T/s

a) The magnitude of the emf induced (E) is given as:

  E= A × (dB/dt)

  on substituting the values in the above equation, we get

E = (0.020 m²) × (0.24 T/s)

or

E = 0.0048 Volts

b) Now, The induced emf when both the area and the magnetic field is varying

we have

E = B(dA/dt) + A(dB/dt)

Now, for the given case induced emf is zero i.e E = 0 and magnetic field B = 2.1 T

thus,

0 = (2.1 T)(dA/dt) + (0.020 m2)(0.24 T/s)

dA/dt = - 0.002285 m²/s

Hence, the area should be decreased at the rate of 0.002285 m²/s