Question

A rigid cirular loop of radius $r$ and mass $m$ lies in the $x-y$ plane on a flat table and has a current $I$. flowing in it. At this particular place, mangetic field is $\overrightarrow{B}=B_x\hat{i}+B_y\hat{j}$. How large must I be so that one edge of loop will lift from table.
Given $m=1kg,r=1m,B_x=3$ Tesla, $B_y=4$ Tesla

• A. $\frac{2}{\pi }A$
• B. $\frac{\pi }{2}A$
• C. $\frac{10}{3\pi }A$
• D. $\pi A$

Answer 1

The correct option is C

$\frac{10}{3\pi }A$

Given that,

Mass $m=1kg$

Radius $r=1m$

Magnetic field $B_x=3T$

Magnetic field $B_y=4T$

Now, the loop will start to lift of the table when

The magnetic torque = the gravitational torque

${\tau }_{mag}={\tau }_{gra}$

$I\pi R^{2}B=mgR$

$I=\frac{mg}{\pi RB}$

$I=\frac{1\times 10}{\pi \times 3\times 1}$

$I=\frac{10}{3\pi }A$

Hence, the current is $\frac{10}{3\pi }A$