A loop carrying current I lies in the x-y plane as shown in the...

A loop carrying current

I

lies in the

x-y

plane as shown in the figure. The unit vector

\hat{k}

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

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

Options

A $a^{2} I \hat{k}$
B $\left(\frac{\pi}{2}+1\right) a^{2} I \hat{k}$
C $-\left(\frac{\pi}{2}+1\right) a^{2} I \hat{k}$
D $(2 \pi+1) a^{2} I \hat{k}$

Correct answer

B. $\left(\frac{\pi}{2}+1\right) a^{2} I \hat{k}$

Step-by-step solution

Magnetic moment of a current carrying loop

\vec{M}=N I \vec{A}

Here

N=1, A=a^{2}+2 \pi

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

\left[1+\frac{\pi}{2}\right]

From Screw law, direction of

m

is outward or in +ve z-direction.

\therefore \quad \vec{M}=I a^{2}\left[1+\frac{\pi}{2}\right] \hat{k}

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