Question

A planar coil having 12 turns carries 15 A current. The coil is oriented with respect to the uniform magnetic field $\vec{B}=0.2\hat{i}T$ such that its directed area is $\vec{A}=-0.04\hat{i}{m}^2$ The potential energy of the coil in the given orientation is

• A. 0
• B. +0.72 J
• C. +1.44 J
• D. -1.44 J

Answer 1

Answer: (C)

Here, $\vec{B}=0.2\hat{i}T;I=15A;N=12$;
$\vec{A}=-0.04\hat{i}{m}^2$
Magnetic moment of the coil $\vec{M}=NI\vec{A}$
$=(12)(15A)\left(-0.04\hat{i}{m}^2\right)=-7,2\hat{i}A{m}^2$
The potential energy of the coil in the given orientation is
$U=-\vec{M}\cdot \vec{B}=-\left(-7.2\hat{i}A{m}^2\right)\cdot (0.2\hat{i}T)$
$=+1.44J$