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JIPMER 2018
Exam
JIPMER
Year
2018
Subject
Physics
Chapter
Magnetic Effects of Current

JIPMER 2018 · Physics · Magnetic Effects of Current

Electron revolving with speed v is producing magnetic field B at...

Electron revolving with speed v is producing magnetic field B at centre. Find relation between radius of path BB and vv ?

Options

  1. AB∝V∝1rB \propto V \propto \frac{1}{r}
  2. BB∝V∝1r2B \propto V \propto \frac{1}{r^2}
  3. CB∝V2∝1rB \propto V^2 \propto \frac{1}{r}
  4. DB∝v2∝1r2B \propto v^2 \propto \frac{1}{r^2}

Correct answer

B. B∝V∝1r2B \propto V \propto \frac{1}{r^2}

Step-by-step solution

∵\because Magnetic field at center, B=\frac{\mu_0\mathrm{I}}{2 \mathrm{r}} where, I=etI=\frac{\mathrm{e}}{\mathrm{t}} or \quad\mathrm{I}=e(2πrv)=ev2πr=\frac{\mathrm{e}}{\left(\frac{2 \pi \mathrm{r}}{\mathrm{v}}\right)}=\frac{\mathrm{ev}}{2 \pi \mathrm{r}} Hence, B=(μ02r)(ev2πr)=μ0ev4πr2B=\left(\frac{\mu_0}{2 \mathrm{r}}\right)\left(\frac{\mathrm{ev}}{2 \pi \mathrm{r}}\right)=\frac{\mu_0 \mathrm{ev}}{4 \pi \mathrm{r}^2} or B∝Vr2\quad B \propto \frac{V}{r^2}
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