First slide

Motional EMF

Question

A square loop of side 1 m is placed in a perpendicular magnetic field. Half of the area of the loop lies inside the magnetic field. A battery of e.m.l 10 V and negligible internal resistance is connected in the loop. [Fig. (3)]. The magnetic field changes
with time according to the relation
B = (0.01 - 2 t) tesla.
The total e.m.f. of the battery will be

Moderate

A

1 V
B

11 V
C

9 V
D

10 V

Solution

See fig. (3). Induced e.m.f. is given by
$\begin{array}{l} e = - \frac{dΦ}{dt} = - \frac{d}{dt} (BA) = - A \frac{dB}{dt} \\ = - \frac{l^{2}}{2} \frac{d}{dt} (0 \cdot 01 - 2 t) \\ = \frac{(1)^{2}}{2} \times 2 = 1 volt \end{array}$

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