First slide

Motional EMF

Question

A rectangular coil of 20 turns and area of cross-section 25 sq. cm has a resistance of 100 $Ω$ . If a magnetic field which is perpendicular to the plane of the coil changes at a rate of 1000 tesla per second, the current in the coil is

Moderate

A

1.0 ampere
B

50 ampere
C

0.5 ampere
D

5.0 ampere

Solution

$e = - \frac{dΦ}{dt} and i = \frac{e}{R} \begin{array}{l} ∴ i = - \frac{1}{R} \frac{dΦ}{dt} = - \frac{1}{R} \frac{d}{dt} (nBA) \\ = - \frac{nA}{R} \frac{dB}{dt} = - \frac{20 \times (25 \times 10^{- 4})}{100} \times 1000 \\ = - 0 \cdot 5 amp = | 0 \cdot 5 | amp \end{array}$
negative sign indicates the direction.

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