Question

A rectangular loop of sides $10$cm and $5$ cm carrying a current $I$ of $12$A is placed in different orientations as shown in the figure below.
If there is a uniform magnetic field of $0.3$T in the positive z-direction, in which 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. $\left(\right)1$ and $\left(2\right)$, respectively
• D. $\left(\right)1$ 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$=-\overrightarrow{\mu }\cdot \overrightarrow{B}$

$=-\overrightarrow{\mu }\cdot \overrightarrow{B}\cos \theta$

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

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

$\therefore$ (1),(3) are not in equilirium.

And (2) is a stable equilibrium, (4) is an unstable equilibrium.