A particle carrying a charge equal to 100 times the charge on an electron is rotating one rotation per…

A particle carrying a charge equal to 100 times the charge on an electron is rotating one rotation per second in a circular path of radius 0.8 m . The value of magnetic field produced at the centre will be ( $\mu_0=$ permeability of vacuum)
  1. $\frac{10^{-7}}{\mu_0}$
  2. $10^{-17} \mu_0$
  3. $10^{-6} \mu_0$
  4. $10^{-7} \mu_0$

Solution

Charged particle moving in a circular path acts like a current carrying coil. Let I be the current due to the particle current is, $I=\frac{q}{t}=\frac{100 \times e}{1}=100 e$
Magnetic field at the centre due to current carrying coil, $\begin{aligned} \mathrm{B}_{\text {centre }} & =\frac{\mu_0}{4 \pi} \frac{2 \pi \mathrm{I}}{\mathrm{r}}=\frac{\mu_0}{4 \pi} \frac{2 \pi \times 100 \mathrm{e}}{\mathrm{r}} \\ & =\frac{\mu_0}{4} \frac{2 \times 100\left(1.6 \times 10^{-19}\right)}{0.8}=10^{-17} \mu_0 \end{aligned}$ .

Asked in: MHT CET 2024 (04 May Shift 2)

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