Question

A rectangular loop of sides $10cm$ and $5cm$ carrying a current $I$ of $12A$ is placed in different orientations as shown in the figure below.


If there is a uniform magnetic field of $0.3T$ in the positive z-direction, the orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium

• A. $\left(2\right)$ and $\left(4\right)$ respectively
• B. $\left(2\right)$ and $\left(3\right)$ respectively
• C. $\left(1\right)$ and $\left(2\right)$ respectively
• D. $\left(1\right)$ and $\left(3\right)$ respectively

Answer 1

The correct option is A $\left(2\right)$ and $\left(4\right)$ respectively

Stable and unstable configuration are determined by the potential energy stored in the system.
Minimum potential energy $\Rightarrow$ stable configuration.
Potential energy $=-\overrightarrow{\mu }\cdot \overrightarrow{B}$
$=-\mu B\cos \theta$

$\theta$ for (1) $={90}^{\circ }$, $\theta$ for (2) $=0^{\circ }$,$\theta$ for (3) $={90}^{\circ }$, $\theta$ for (4) $={180}^{\circ }$

$\therefore$ U $=0$ for (1)
U $=-\mu B$ for (2)
U $=0$ for (3)
U $=\mu B$ for (4)

$\therefore$ (2) is most stable, (4) is unstable.