This question is incomplete, the complete question is;
A magnetic field is passing through a loop of wire whose area is 0.015 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 0.20 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 = 1.5 T, if the induced emf is to be zero? (Give the magnitude of the rate of change of the area.) (m2/s)
Answer:
a) the magnitude of the emf induced in the loop is 0.003 V
b) dA/dt = 0.002 m²/s
Explanation:
Area of the loop wire A = 0.015 m²
magnitude of the field is increasing dB/dt = 0.20 T/s
a)
Determine the magnitude of the emf induced in the loop.
V = A( dB/dt )
we substitute
V = 0.015 m² × 0.20 T/s
V = 0.003 V
Therefore, the magnitude of the emf induced in the loop is 0.003 V
b) the induced emf is;
V = B( dA/dt ) + A( dB/dt )
given that; induced emf is 0, B = 1.5
so we substitute
0 = [ 1.5T × ( dA/dt ) ] + [ 0.015 m² × 0.20 T/s ]
-[ 1.5T × ( dA/dt )] = 0.003 m²T/s
dA/dt = -[ 0.003 m²T/s / 1.5T ]
dA/dt = -0.002 m²/s
the negative shows that the area is decreasing
hence, dA/dt = 0.002 m²/s
