Question

A current carrying square loop is placed near an infinitely long current carrying wire as shown in figure. The torque acting on the loop is

• A. $\frac{{\mu }_0}{2\pi }\left(\frac{i_1{i}_{2}a}{2}\right)$
• B. $\left(\frac{{\mu }_0{i}_1{i}_{2}a}{2\pi }\right)$
• C. $\left(\frac{{\mu }_0{i}_1{i}_{2}a}{2\pi }\right)\ln 2$
• D. zero

Answer 1

The correct option is D zero

Magnetic field due to current carrying infinite long wire is shown in figure.


Magnetic moment of square loop $\overrightarrow{\mu }=i_2{a}^2(-\hat{k})$

Torque acting on the square loop $\overrightarrow{\tau }=\overrightarrow{\mu }\times \overrightarrow{B}$

$\Rightarrow \overrightarrow{\tau }=i{a}^2(-\hat{k})\times \frac{{\mu }_{0}i}{2\pi a}(-\hat{k})=0$

Hence, option (d) is the correct answer.