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

Answer 1

Answer: (B)

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