Question

A loop $ABCD$ is moving with velocity $v$ towards the right. The magnetic field is $2T$ . Loop is connected to a resistance of $9\Omega$ . If the steady current of $2A$ flows in the loop, then the value of $v$ , if loop has resistance of $4\Omega$ , is (Given $AD=30cm$ )

• A. $86.7m{s}^{-1}$
• B. $30m{s}^{-1}$
• C. $33.33m{s}^{-1}$
• D. $20m{s}^{-1}$

Answer 1

Answer: (A)

When a straight conductor moves with velocity v perpendicular to the magnetic field then emf induced is given by $V=Bvl$ . Here, it will be $V=Bv(lsin\theta )$ .
Potential difference is $V=Bv(lsin\theta )$
$V=2\times v\times \frac{30}{100}\times \frac{1}{2}=0.3v$
Now, $\text{Current}=\frac{\text{V}}{\text{R}}$
$\Rightarrow 2=\frac{0.3v}{13}$
$\Rightarrow v=86.7{\text{ m s}}^{-1}$