Question

A non-conduction rod $AB$ of length $l$ has a total charge $q$. The rod is rotated about an axis passing through its center of mass with a constant angular velocity $\omega$ as shown in the figure. The magnetic moment of the rod is

• A. $\frac{q\omega l^2}{12}$
• B. $\frac{q\omega l^2}{3}$
• C. $\frac{q\omega l^2}{24}$
• D. $\frac{q\omega l^2}{6}$

Answer 1

The correct option is A $\frac{q\omega l^2}{12}$

Given : A non-conduction rod ABAB of length ll has a total charge qq. The rod is rotated about an axis passing through its center of mass with a constant angular velocity ωω as shown in the figure.

Solution :

We have a relation between magnetic moment $\mu$ and angular momentum L

That is $\frac{\mu }{L}=\frac{q}{2m}$

q= charge. m=mass

Angular momentum of rod through com= $\frac{m\omega l^2}{12}$

substituting all the values in the relation we get $\mu =\frac{qw{l}^2}{12}$

The Correct Opt = A