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 0.19 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 = 1.6 T if the induced emf is to be zero? (Give the magnitude of the rate of change of the area.) (m^2/s). Explain whether the area is to be enlarged or shrunk.

Answer 1

a. 0.00266v

b. -0.0016625

the area should be shrunk

Step-by-step explanation:

the magnitude of the EMF induced in the loop

= area * rate

= 0.014 * 0.19

= 0.00266 V

B we are to solve for the rate at which the are has to be change with B = 1.6

δA/δt = -A/B * dB/dt

= (-0.014 * 0.19) /1.6

= -0.0016625

the sign is negative so the EMT is negative and so the area has to be shrunk.