Question

Two parallel long straight conductors lie on a smooth plane surface. Two other parallel conductors rest on them at right angles so as to form a square of side $a$. A uniform magnetic field $B$ exists at right angles to the plane containing the conductors. Now conductors start moving outward with a constant velocity $v_0$ at $t=0$. Then induced current in the loop at any time $t$ is ($\lambda$ is resistance per unit length of the conductors) :

• A. $\frac{aB{v}_0}{\lambda (a+v_{0}t)}$
• B. $\frac{aB{v}_0}{2\lambda }$
• C. $\frac{B{v}_0}{\lambda }$
• D. $\frac{B{v}_0}{2\lambda }$

Answer 1

The correct option is C $\frac{B{v}_0}{\lambda }$

At $t=t$ side of square,
$l=(a+2v_{0}t)$
Area $S=l^2={(a+2v_{0}t)}^2$
$\varphi =BS=B{(a+2v_{0}t)}^2$
$e=\frac{d\varphi }{dt}=4B{v}_0(a+2v_{0}t)$
$R=\lambda \left[4l\right]=4\lambda (a+2v_{0}t)$
$\therefore$ $i=\frac{e}{R}=\frac{B{v}_0}{\lambda }$