First slide

Motional EMF

Question

A square loop of side 4 cm is lying on a horizontal table. A uniform magnetic field of 0.5 T is directed towards at an angle of 60^o to the vertical as shown in fig. If the field increases from zero to its final
value in 0.2 s, the e.m.f. induced in the loop will be

Moderate

A

2 mV
B

4 mV
C

6 mV
D

8 mV

Solution

Charge in magnetic flux = A B cos $θ$
$dΦ = {(4 \times 10^{- 2})}^{2} \times 0 \cdot 5 \times \cos 60^{\circ} or dΦ = 0 \cdot 4 \times 10^{- 3} Wb Now e = \frac{dΦ}{dt} = \frac{0 \cdot 4 \times 10^{- 3}}{0 \cdot 2} = 2 \times 10^{- 3} V$
= 2mV.

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