Question

A thin circular ring of radius r and mass m lies on the x-y plane on a flat table and carries a current i in the presence of the earth's magnetic field given by $B=B_x\hat{i}+B_z\hat{k}.$The value of i so that the ring just lifts from the table about its edge is

• A. $\frac{mg}{\pi r{B}_x}$
• B. $\frac{mg}{\pi r\sqrt{B_x^2}+B_z^2}$
• C. $\frac{mg}{\pi r{B}_z}$
• D. $\frac{mg}{2\pi r\sqrt{B_x^2}+B_z^2}$

Answer 1

The correct option is A $\frac{mg}{\pi r{B}_x}$

$Given:$ $B=B_x\hat{i}+B_z\hat{k}$

$Solution:$

Net Torque is $\tau =-M{B}_x\hat{j}$ $|\tau |=I\pi r^2{B}_x$

By torque balance $mgr=\tau$

$mgr=I\pi r^{2}Bx$

$I=\frac{mg}{\pi r{B}_x}$

$So,the$ $correct$ $option:A$