A square loop of side 20 cm and resistance 1 Ω is moved towards right with a constant speed v 0 . The right arm of the loop is in a uniform magnetic field of 5 T . The field is perpendicular to the pl

Question

A square loop of side 20 cm and resistance 1 Ω is moved towards right with a constant speed v 0 . The right arm of the loop is in a uniform magnetic field of 5 T . The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value 4 Ω . What should be the value of v 0 so that a steady current of 2 mA flows in the loop ?

TestHub · Accepted Answer

The EMF is induced in the coil when it is moving in a uniform magnetic field,
$e = B v l$ and the current, $i = \frac{e}{R}$ $\Rightarrow$ $\frac{B l v}{R} = 0.002 A$
$\Rightarrow v = \frac{0.002 \times R}{B l}$ $= \frac{0.002 \times (4 + 1)}{5 \times 0.2} = 0.01 m s^{- 1} = 1 cm s^{- 1}$ .

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