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
$U=-\vec{M} \cdot \vec{B}$
$=-\left(-7.2 \hat{i} A m^{2}\right) \cdot(0.2 \hat{i} T)$
$=+1.44\, J$