First slide

Magnetic flux and induced emf

Question

A square metallic wire loop of side 0.1 m and resistance of 1 $Ω$ is moved with a constant velocity in a magnetic field of 2 wb/m² as shown in figure. The magnetic field is perpendicular to the plane of the loop, loop is connected to a network of resistances. What should be the velocity of loop so as to have a steady current of 1mA in loop

Moderate

A

1 cm/sec
B

2 cm/sec
C

3 cm/sec
D

4 cm/sec

Solution

Equivalent resistance of the given Wheatstone bridge circuit (balanced) is 3 $Ω$ so total resistance in circuit is $R = 3 + 1 = 4 Ω$ . The emf induced in the loop $e = Bvl$ .
So induced current $i = \frac{e}{R} = \frac{Bvl}{R}$
$\Rightarrow 10^{- 3} = \frac{2 \times v \times (10 \times 10^{- 2})}{4} \Rightarrow v = 2 cm / \sec .$

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