An electron (e) moves in circular orbit of radius ' $r$ ' with uniform speed ' $\mathrm{V}$ '. It produces…

An electron (e) moves in circular orbit of radius ' $r$ ' with uniform speed ' $\mathrm{V}$ '. It produces magnetic field ' $\mathrm{B}$ ' at the center of circle. The magnetic field $B$ is ( $\mu_0=$ permeability of free space)
  1. $\frac{\mu_0 \mathrm{e}}{4 \pi}\left(\frac{\mathrm{V}}{\mathrm{r}^2}\right)$
  2. $\frac{\mu_0 \mathrm{e}}{4 \pi} \mathrm{Vr}^2$
  3. $\frac{\mu_0 \mathrm{e}}{4 \pi}\left(\frac{\mathrm{V}}{\mathrm{r}}\right)$
  4. $\frac{\mu_0 \mathrm{e}}{4 \pi} \mathrm{Vr}$

Solution

Magnetic field at the center of a circular coil is given by $\mathrm{B}=\frac{\mu_0 \mathrm{I}}{2 \mathrm{r}}$ In this case, the current $\mathrm{I}=\frac{\mathrm{e}}{\mathrm{T}}=\frac{\mathrm{eV}}{2 \pi \mathrm{r}}$ $\mathrm{B}=\frac{\mu_0 \mathrm{eV}}{4 \pi \mathrm{r}^2}$

Asked in: MHT CET 2021 (20 Sep Shift 2)

Practice more Magnetic Fields due to Electric Current questions on Aicharya