Question

A magnetic B field of strength 4 T is perpendicular to a conducting loop of wire measuring 0.4 square meters with 50 turns. If the B field is linearly reduced to zero in 2 s, then what is the magnitude of the induced emf voltage? (in units of V)

Answer 1

Magnetic flux, $\large \phi=BAN$

where B is the magnetic field,A is the area of the loop and N is the number of turns.

Here,

Initial magnetic field, $\large B_0= 4 T$

Area of the loop = 0.4 $\large m^2$

number of turns, N = 50

Final magnetic field, $\large B_t=0$

Time , t = 2s

Now,

Initial magnetic flux, $\large \phi_1 = B_0AN =4\times 0.4\times 50 = 80 Wb$

Final magnetic flux, $\large \phi_2 = B_tAN =0\times 0.4\times 50 = 0$

Induced voltage = $\large \frac{\phi_1-\phi_2}{t}=\frac{80-0}{2}=40V$