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