MHT CET · Physics · Atomic Physics
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)
- A \(\frac{\mu_{0} \mathrm{eL}}{4 \pi m r^{2}}\)
- B \(\frac{\mu_{0} \mathrm{eL}}{4 \pi m r^{3}}\)
- C \(\frac{\mu_{0} \mathrm{eL}}{2 \pi \mathrm{mr}^{2}}\)
- D \(\frac{\mu_{0} \mathrm{eL}}{2 \pi m r^{3}}\)
Answer & Solution
Correct Answer
(B) \(\frac{\mu_{0} \mathrm{eL}}{4 \pi m r^{3}}\)
Step-by-step Solution
Detailed explanation
\(\frac{B}{L}=\frac{\mu_{0}}{4 \pi} \frac{\frac{e V}{r^{2}}}{m V r} L=m V r\)
\(\frac{B}{L}=\frac{\mu_{0}}{4 \pi} \frac{e V}{e^{2}} \times \frac{1}{m V r}\)
\(\Rightarrow B=\frac{\mu_{0}}{4 \pi} \frac{L}{r}=\frac{\mu_{0} e L}{4 \pi m r^{3}}\)
\(\frac{B}{L}=\frac{\mu_{0}}{4 \pi} \frac{e V}{e^{2}} \times \frac{1}{m V r}\)
\(\Rightarrow B=\frac{\mu_{0}}{4 \pi} \frac{L}{r}=\frac{\mu_{0} e L}{4 \pi m r^{3}}\)
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