Question

A current carrying loop is placed in a uniform magnetic field, in four different orientations $I,II,III$ and $IV$. Arrange all of them in decreasing order of their potential energy.

• A. $I>III>II>IV$
• B. $I>II>III>IV$
• C. $I>IV>II>III$
• D. $III>IV>I>II$

Answer 1

The correct option is C $I>IV>II>III$

Potential energy of a current loop in a uniform magnetic field is given by,

$U=-\overrightarrow{m}.\overrightarrow{B}=-mB\cos \theta$

For orientation $I$, ${\theta }_1={180}^{\circ }$

So, $U_I=mB$

For orientation $II$, ${\theta }_2={90}^{\circ }$

So, $U_{II}=0$

For orientation $III$, $0^{\circ }<{\theta }_3<{90}^{\circ }$

So, $-mB<U_{III}<0$

For orientation $IV$, ${90}^{\circ }<{\theta }_4<{180}^{\circ }$

​​​​​​​So, $0<U_{IV}<mB$

Therefore, $I>IV>II>III$

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

Why this question? To understand the concept of potential energy of a current carrying coil in a magnetic field.