Question

Consider the expression for magnetic potential energy, match the terms of Column I with the items of Column II and choose the correct option from the codes given below.

Column I		Column II
A	Potential energy at $\theta =90^{\circ }$	1	Minimum
B	Potential energy at $\theta =0^{\circ }$	2	Maximum
C	Potential energy at $\theta =180^{\circ }$	3	Zero

• A. A-(3), B-(1), C-(2)
• B. A-(1), B-(2), C-(3)
• C. A-(2), B-(1), C-(3)
• D. A-(1), B-(3), C-(2)

Answer 1

Answer: (A)

Since, the magnetic potential energy $U_m$ is given by,
$U_m=m\cdot B=-mB\cos \theta$
A. For $\theta =90^{\circ }$,
$U_m=-mB\cos 90^{\circ }=0$
B. For $\theta =0^{\circ }$,
$U_m=-mB\cos 0^{\circ }=-mB$
The potential energy is minimum and hence the needle is in most stable position.
C. For $\theta =180^{\circ }$,
$U_m=-mB\cos 180^{\circ }=+mB$
The potential energy is maximum and hence the needle is in unstable position.