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