A loop carrying current lies in the plane as shown in the figure. The unit vector is coming out of the plane of the paper. The magnetic moment of the current loop is [2012]

Question

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 [2012]

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(2)

Magnetic moment of a current-carrying loop $\vec{M} = N I \vec{A}$

Here, $N = 1,$ $A = a^{2} + 2 π {(\frac{a}{2})}^{2} = a^{2} (1 + \frac{π}{2})$

From the screw law, the direction of $m$ is outward or in the positive $z$ -direction.

$∴$ $\vec{M} = I a^{2} (1 + \frac{π}{2}) \hat{k}$

Solution

Q.
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 [2012]

1 $a^{2} I \hat{k}$

2 $(\frac{π}{2} + 1) a^{2} I \hat{k}$

3 $- (\frac{π}{2} + 1) a^{2} I \hat{k}$

4 $(2 π + 1) a^{2} I \hat{k}$

Ans.
(2)

Magnetic moment of a current-carrying loop $\vec{M} = N I \vec{A}$

Here, $N = 1,$ $A = a^{2} + 2 π {(\frac{a}{2})}^{2} = a^{2} (1 + \frac{π}{2})$

From the screw law, the direction of $m$ is outward or in the positive $z$ -direction.

$∴$ $\vec{M} = I a^{2} (1 + \frac{π}{2}) \hat{k}$

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Solution

Q. 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 the paper. The magnetic moment of the current loop is [2012]

1 a2Ik^

2 (π2+1)a2Ik^

3 -(π2+1)a2Ik^

4 (2π+1)a2Ik^