Question

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is $d(>>a)$. If the loop applies a force $F$ on the wire then :

• A. $F\propto \left(\frac{a^2}{d^3}\right)$
• B. $F\propto \left(\frac{a}{d}\right)$
• C. $F\propto {\left(\frac{a}{d}\right)}^2$
• D. $F=0$

Answer 1

Answer: (C)

$F\propto {\left(\frac{a}{d}\right)}^2$

Eqvilent dipole of given loop
$F=m\cdot \frac{dB}{dr}$
Now, $\frac{dB}{dx}=\frac{d}{dx}\left(\frac{{\mu }_{0}I}{2\pi x}\right)$
$\propto \frac{1}{x^2}$
$\Rightarrow$ So $F\propto \frac{M}{x^2}[\therefore M=NIA]$
$F\propto \frac{a^2}{d^2}$