Question
Define the term magnetic moment of a current loop. Write the expression for the magnetic moment when an electron revolves at a speed v around an orbit of radius ‘r’ in hydrogen atom.
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Answer
Magnetic moment of a current loop:
The torque on current loop is
$\tau=\text{MB}\sin\theta$, where $\theta$ is angle between magnetic moment and magnetic field.$\Rightarrow\text{M}=\frac{\tau}{\text{B}\sin\theta}$
If B or 1 T, $\sin\theta=1$ or $\theta=90^\circ$ then $\text{M}=\tau$.
That is the magnetic moment of a current loop is defined as the torque acting on the loop when placed in a magnetic field of 1 T such that the loop is oriented with its area vector normal to the magnetic field.
Also, M = IA
i.e., magnetic moment of a current loop is the product of current flowing in the loop and area of loop. Its direction is perpendicular to the plane of the loop and determined by using right hand thumb rule.
Magnetic moment of revolving electron,
$\text{M}=\frac{\text{evr}}{2}$
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