A wire of length L metre carrying a current I ampere is bent in the form of a circle. The magnitude of its magnetic moment is :

Question

A wire of length L metre carrying a current I ampere is bent in the form of a circle. The magnitude of its magnetic moment is : (A)  IL2/4π  (B)  I2L2/4π  (C)  I2L/8π  (D)  IL2/8π

Tardigrade Admin · Accepted Answer

If r is the radius of circle then L=2 π r or r=(L/2 π) ∴ Area =π r2 =π L2 / 4 π2=(L2/4 π) Now magnetic moment M=N i A =I L2 / 4 π

Q. A wire of length $L$ metre carrying a current $I$ ampere is bent in the form of a circle. The magnitude of its magnetic moment is :

$I L^{2} /4 π$

$I^{2} L^{2/} 4 π$

$I^{2} L /8 π$

$I L^{2} /8 π$

If $r$ is the radius of circle then $L = 2 π r$
or $r = \frac{L}{2 π}$
$∴$ Area $= π r^{2}$
$= π L^{2} /4 π^{2} = \frac{L ^{2}}{4 π}$
Now magnetic moment $M = N i A$
$= I L^{2} /4 π$

Q. A wire of length L metre carrying a current I ampere is bent in the form of a circle. The magnitude of its magnetic moment is :

IL2/4π

I2L2/4π

I2L/8π

IL2/8π