Question

A super conductig square rigid frame of mass $m$, self inductance $L$ and side $a$ is cooled down (in a magnetic field) to a temperature below the critical temperature. The frame is kept horizontal (parallel to the x-y plane) and constarined to move in the z- direction in a non - uniform but constant magnetic field given by $\overrightarrow{B}=-\alpha x\hat{i}+(\alpha z+B_0)\hat{k}$ and a uniform gravitational field given by accelaration $-g\hat{k}$ as shown in figure. The thickness of the frame is much smaller than $a$. Initially the frame is at rest with its centre conciding with the origin. Now the frame is released at $t=0.$
Maximum magnitude of Z - cordinate of centre of loop during subsquent motion will be

• A. $\frac{mgL}{{\alpha }^2{a}^4}$
• B. $\frac{2mgL}{{\alpha }^2{a}^4}$
• C. $\frac{3mgL}{{\alpha }^2{a}^4}$
• D. $\frac{4mgL}{{\alpha }^2{a}^4}$

Answer 1

The correct option is A $\frac{mgL}{{\alpha }^2{a}^4}$

$\frac{mgL}{{\alpha }^2{a}^4}$