A conducting square loop of side L and resistance R moves in its...

A conducting square loop of side

\mathrm{L}

and resistance

\mathrm{R}

moves in its plane with a uniform velocity v perpendicular to one of its side. A magnetic induction

\mathrm{B}

constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere. A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one

A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one

The current induced in the loop is

Options

A $\frac{\mathrm{B} \ell \mathrm{v}}{\mathrm{R}}$ clockwise
B $\frac{\mathrm{B} \ell \mathrm{v}}{\mathrm{R}}$ anticlockwise
C $\frac{2 \mathrm{ B} \ell v}{\mathrm{R}}$ anticlockwise
Dzero

Correct answer

D. zero

Step-by-step solution

Since the magnetic field is uniform the flux

f

through the square loop at any time

t

is constant, because

\begin{array}{l} \mathrm{f}=\mathrm{B} \times \mathrm{A}=\mathrm{B} \times \mathrm{L}^{2}=\text{ constant } \\ \therefore \varepsilon=-\frac{\mathrm{d} \phi}{\mathrm{dt}}=\text{ zero } \end{array}

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