Question

A circular current carrying loop with magnetic moment parallel to the magnetic field is rotated by an angle of $90^{\circ }$ slowly about one of its diameter in a uniform magnetic field. Match the quantities of Column I with Column II.

Column I		Column II
A	Torque on the loop	1	Decreases from maximum to zero.
B	Potential energy of the loop	2	Remains constant
C	Magnetic moment of the loop	3	Increases from zero to maximum
D	Magnetic flux through the loop	4	Increases from minimum to zero.

• A. (A) $\to$ (2); (B) $\to$ (1); (C) $\to$ (3); (D) $\to$ (4)
• B. (A) $\to$ (3); (B) $\to$ (4); (C) $\to$ (2); (D) $\to$ (1)
• C. (A) $\to$ (4); (B) $\to$ (3); (C) $\to$ (2); (D) $\to$ (1)
• D. (A) $\to$ (2); (B) $\to$ (1); (C) $\to$ (4); (D) $\to$ (3)

Answer 1

Answer: (B)

(A) $\to$ (3) ; (B) $\to$ (4); (C) $\to$ (2); (3) $\to$ (1)
(A) $I=mB\sin \theta$, as $\sin \theta$ from $0\to 1$.
(B) $U(\theta )=-mB\cos \theta$, as $\cos \theta$ from I $\to 0$, then $U(\theta )$ from $U(\theta {)}_{\min }=-mB\to 0$.
(C) $s\vec{m}=i\vec{A}$.
(D) as ${\varphi }_B=BA\cos \theta$. As $\cos \theta$ from $1\to 0$, then ${\varphi }_B$ from $BA={\left({\varphi }_B\right)}_{\max }\to 0$.