Question

A conducting ring of radius R, mass M and carrying current I in anticlockwise direction as seen from top hangs, with its plane parallel to horizontal plane, by two non-conducting strings as shown in the figure. The uniform horizontal magnetic field B exists is the region. If both strings are tight and the ring is in equilibrium, find the minimum tension in the any string.

• A. $\frac{(2IRB+Mg)}{2}$
• B. $\frac{Mg}{2}$
• C. $\frac{(I\pi RB+Mg)}{2}$
• D. $\frac{(Mg-\pi IRB)}{2}$

Answer 1

The correct option is D $\frac{(Mg-\pi IRB)}{2}$

By moment equilibrium about C,
$T_1\left(2R\right)-MgR+\left(I\pi R^2\right)B=0$
$\Rightarrow T_1=\frac{(Mg-\pi IRB)}{2}$