Question

A square metallic wire loop of side 0.1 m and resistance of 1Ω 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

• A. 1 cm/sec
• B. 2 cm/sec
• C. 3 cm/sec
• D. 4 cm/sec

Answer 1

Answer: (B)

2 cm/sec

Answer 2

Equivalent resistance of the given Wheatstone bridge circuit (balanced) is 3Ω so total resistance in circuit is $R = 3 + 1 = 4\Omega$. The emf induces in the loop $e = Bvl$.

So induced current

$i = \frac{e}{R} = \frac{Bvl}{R} \Rightarrow 10^{- 3} = \frac{2 \times v \times (10 \times 10^{- 2})}{4} \Rightarrow v = 2cm/sec.$