Question

A uniform magnetic field $\overline{B}=B_0\overline{k}$ is acting in the region where a circular current carrying loop is placed in x-y plane. Match the columns.

	column I		Column II
(A)	Equilibrium of loop	(p)	Along z-axis
(B)	torque of the loop	(q)	Zero
(C)	Magnetic moment of the loop	(r)	Stable
(D)	Potential energy of loop	(s)	None of the above

Answer 1

A current carrying loop along $x-y$ plane where magnitude field exist in $z-$ direction $\overrightarrow{B}=\overrightarrow{B}o\hat{k}$

vectors $\overrightarrow{B}$ and $\overrightarrow{A}$ are along same direction

so,

zarque $=I(\overrightarrow{B}\times \overrightarrow{A})=0$

Magnitude energy $\overrightarrow{M}=I\overrightarrow{A}$, along $z-$axis

Potential energy $u=-\overrightarrow{M}.\overrightarrow{B}$ would be $(\ast -ve)$

and $z=0$ & $u<0$ implise atable equilibrium

$\therefore$ combination: $\left(A\right)\to \left(r\right)\left(B\right)\to \left(q\right)\left(C\right)\to \left(p\right)\left(D\right)\to \left(s\right)$