Discussion Forum



1)

A loop carrying current / lies in the x-y plane as shown in the figure. The unit vector k is coming out of the plane of the paper. The magnetic moment of the current loop is

9112021824_k21.PNG


A) $a^{2}Ik$

B) $\left(\frac{\pi}{2}+1\right)a^{2}Ik$

C) $-\left(\frac{\pi}{2}+1\right)a^{2}Ik$

D) $(2 \pi +1)a^{2}Ik$

Answer:

Option B

Explanation:

Area of the given loop is

 A=(area of two circles of radius $\frac{a}{2}$  and area ofa square of side a )

  $=2 \pi\left(\frac{a}{2}\right)^{2}+a^{2}$

 $=\left(\frac{\pi}{2}+1\right)a^{2}$

$|M|=IA=\left(\frac{\pi}{2}+1\right)a^{2}I$

From screw law direction of M is outwards or in positive z-direction

$\therefore$   M=$\left(\frac{\pi}{2}+1\right)a^{2}Ik$