Question

A uniform rod of length L is charged uniformly with charge q and is rotating about an axis passing through its center. And perpendicular to the rod. Magnetic moment of the rod is-

• A. $\frac{q{L}^2\omega }{6}$
• B. $\frac{q{L}^2\omega }{12}$
• C. $\frac{q{L}^2\omega }{24}$
• D. $\frac{q{L}^2\omega }{36}$

Answer 1

The correct option is C $\frac{q{L}^2\omega }{24}$

Given :A uniform rod of length L is charged uniformly with charge q and is rotating about an axis passing through its center. And perpendicular to the rod.

Solution :

We have a relation between magnetic moment and angular momentum as $\frac{\mu }{L_a}=\frac{q}{2m}$

Where $\mu$ is magnetic moment and and $L_a$ is angular momentum and m is mass.

$L_a$=$\frac{m{L}^2\omega }{12}$

Substituting all the values in the above relation we get $\mu$=$\frac{q\omega L^2}{24}$

The Correct Opt: C