Question

The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is

• A. $\gamma BQ{R}^2$
• B. $-\gamma BQ{R}^2$
• C. $\gamma \frac{BQ{R}^2}{2}$
• D. $-\gamma \frac{BQ{R}^2}{2}$

Answer 1

The correct option is D $-\gamma \frac{BQ{R}^2}{2}$


$B$ along ($+Z$ axis)
$M=\gamma L=\gamma m\omega R^2$
(where $m=$ mass of charged particle)
$M=\gamma m\omega R^2$
$M$ will change due to change in $\omega$.Change in $\omega$ is given by $\left|\begin{array}{c}d\omega \end{array}\right|=\frac{B\theta }{2m}$
Change in $M=\gamma .m\frac{BQ}{2m}{R}^2=\frac{-\gamma BQ{R}^2}{2}$
Negative sign shows change is possible to direction of $B$.