An electron of mass 'm' is revolving around the nucleus in a circular orbit of radius 'r' has angular…

An electron of mass 'm' is revolving around the nucleus in a circular orbit of radius 'r' has angular momentum 'L'. The magnetic field produced by the electron at the centre of the orbit is (e $=$ electric charge, $\mu_{0}=$ permeability of free space)
  1. $\frac{\mu_{0} \mathrm{eL}}{4 \pi m r^{2}}$
  2. $\frac{\mu_{0} \mathrm{eL}}{4 \pi m r^{3}}$
  3. $\frac{\mu_{0} \mathrm{eL}}{2 \pi \mathrm{mr}^{2}}$
  4. $\frac{\mu_{0} \mathrm{eL}}{2 \pi m r^{3}}$

Solution

$\frac{B}{L}=\frac{\mu_{0}}{4 \pi} \frac{\frac{e V}{r^{2}}}{m V r} L=m V r$ $\frac{B}{L}=\frac{\mu_{0}}{4 \pi} \frac{e V}{e^{2}} \times \frac{1}{m V r}$ $\Rightarrow B=\frac{\mu_{0} e L}{4 \pi m r^{3}}$

Asked in: MHT CET 2020 (14 Oct Shift 2)

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