Question

A charged particle going around in a circle can be considered to be a current loop. A particle of mass $m$ carrying charge $q$ is moving in a plane with speed $v$ under the influence of magnetic field $\vec{ B }$. The magnetic moment of this moving particle :

• A. $-\frac{ mv ^{2} \vec{ B }}{ B ^{2}}$
• B. $-\frac{m v^{2} \vec{ B }}{2 \pi B^{2}}$
• C. $\frac{ mv ^{2} \vec{ B }}{2 B ^{2}}$
• D. $-\frac{m v^{2} \vec{ B }}{2 B ^{2}}$

Answer 1

Answer: (D)

Magnetic moment
$M = i A$
$M =\left(\frac{ q }{ T }\right) \times \pi r ^{2}=\frac{ q \pi r ^{2}}{\left(\frac{2 \pi r }{ v }\right)}=\frac{ qvr }{2}$
$M =\frac{ qv }{2} \times \frac{ vm }{ qB }$
$M =\frac{ mv ^{2}}{2 B }$
As we can see from the figure, direction of magnetic moment (M) is opposite to magnetic field
$\vec{ M }=-\frac{ mv ^{2}}{2 B } \hat{ B }$
$=-\frac{ mv ^{2}}{2 B ^{2}} \vec{ B }$