Question

A rigid circular loop of radius $r$ and mass $m$ lies in the $x-y$ plane of a flat table and has a current $i$ flowing in it. At this particular place, the Earth's magnetic field is $\overset{ \rightarrow }{B}=B_{x}\hat{i}+B_{z}\hat{k}$ . The value of $i$ , so that the loop starts tilting, is

• A. $\frac{m g}{\pi \sqrt{B_{x}^{2} + B_{2}^{2}}}$
• B. $\frac{m g}{\pi r B_{x}}$
• C. $\frac{m g}{\pi r B_{z}}$
• D. $\frac{m g}{\pi r \sqrt{B_{x} B_{z}}}$

Answer 1

Answer: (B)

$\overset{ \rightarrow }{M}=i\left(\pi r^{2}\right)\hat{k}$ ,
$ \, \overset{ \rightarrow }{B}=B_{x}\hat{i}+B_{z}\hat{k}$
To start tilting
$\tau_{d u e \, t o \, m a s s}=\tau_{m a g n e t i c}$
$\left|\left(m g\right) r\right|=\left| \, \overset{ \rightarrow }{M} \times \, \overset{ \rightarrow }{B}\right|$
$\left(m g\right) \, \left(r\right)=i\left(\pi r^{2}\right)\left(B_{x}\right)$
$i=\frac{m g}{\pi r B_{x}}$