Exam

JIPMER

Year

2018

Subject

Physics

Chapter

Magnetic Effects of Current

JIPMER 2018 · Physics · Magnetic Effects of Current

The magnetic moment of an electron orbiting in a circulate orbit of...

The magnetic moment of an electron orbiting in a circulate orbit of radius $r$ with a speed $v$ is equal to

Step-by-step solution

Magnetic moment $\mathrm{M}=\mathrm{NiA}$ where, $\mathrm{N}=$ number of turns of the current loop and $\mathrm{i}=$ current. Since, the orbiting electron behaves as a current loop of current $i$, we can write $\mathrm{i}=\frac{\mathrm{e}}{\mathrm{T}}=\frac{\mathrm{e}}{\frac{2 \pi \mathrm{r}}{\mathrm{V}}}=\frac{\mathrm{ev}}{2 \pi \mathrm{r}}$ where, $\mathrm{A}=$ area of the loop $=\pi \mathrm{r}^2$. $\Rightarrow \quad M=(1)\left(\frac{\mathrm{ev}}{2 \pi \mathrm{r}}\right)\left(\pi \mathrm{r}^2\right)=\frac{\mathrm{evr}}{2}$