Question

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

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

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 $V=Bv\left(\right.lsin\theta \left.\right)$ .
Potential difference is $V=Bv\left(\right.lsin\theta \left.\right)$
$V=2\times v\times \frac{3 0}{1 0 0}\times \frac{1}{2}=0\cdot 3v$
Now, $\text{Current}=\frac{\textit{V}}{\textit{R}}$
$\Rightarrow 2=\frac{0 \cdot 3 V}{13}$
$\Rightarrow v=86.7\text{ m s}^{- 1}$