Question

A rectangular loop of sides $10\text{cm}$ and $5\text{cm}$ carrying a current $I$ of $2\text{A}$ is placed in different orientations as shown in figure below. Assume the magnetic field to be uniform.

(i)

(ii)

(iii)

(iv)

In which orientation the loop is in equilibrium position?

• A. $\left(i\right)$ & $\left(ii\right)$
• B. $\left(ii\right)$ & $\left(iv\right)$
• C. $\left(i\right)$& $\left(iii\right)$
• D. $\left(ii\right)$& $\left(iii\right)$

Answer 1

The correct option is B $\left(ii\right)$ & $\left(iv\right)$

Since in all four cases the loop is placed in uniform $\overrightarrow{B}$ and it is a closed loop.

$\Rightarrow F_{net}=0$

Force due to magnetic field is zero

However for torque on loop is given by,

$\overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B}$

For equilibrium position of loop
${\overrightarrow{F}}_{net}=0$ & $\overrightarrow{\tau }=0$

$\overrightarrow{\tau }=MB\sin \theta$

Thus $\tau =0$ is possible, when $\theta =0^{\circ }$ or $\theta ={180}^{\circ }$, where $\theta$ is the angle between magnetic moment vector & magnetic field.



Thus, the orientation shown in the figure $\left(ii\right)$ & $\left(iv\right)$ represent equilibrium position.

Hence, option $\left(B\right)$ is the correct answer.