Question

A square metal wire loop of side 10 cm and resistance 1 $\Omega$ is moved with a constant velocity v in a uniform magnetic field B = 2 T, as shown in Fig. 25.4. The loop is connected to 4 $\Omega$ resistor.
What should be the speed v of the loop as to have a steady current of 1 mA in the loop ?

• A. $1cm{s}^{-1}$
• B. $2cm{s}^{-1}$
• C. $3cm{s}^{-1}$
• D. $4cm{s}^{-1}$

Answer 1

The correct option is B

$2cm{s}^{-1}$

The emf induced by a wire of length l moving a field B with speed v perpendicular to the field is given by $e=Blv=2\times 0.1\times v=0.2v$
Current in the circuit is $I=\frac{e}{R}=\frac{0.2v}{4}.ButI=1mA={10}^{-3}A.$ Therefore,
${10}^{-3}=\frac{0.2v}{4}$
which gives $v=2\times {10}^{-2}m{s}^{-1}=2cm{s}^{-1}$.