Question

A particle carrying a charge equal to 1000 times the charge on an electron, is rotating at one rotation per second in a circular path of radius 0.4 m. The value of the magnetic field produced at the centre will be (in tesla) (μ₀ = permeability of vacuum, e = 1.6 × 10⁻¹⁹ C)

विकल्प

• \[2\mu_0\times10^{-16}\]

• \[\mu_0\times10^{-16}\]

• \[\frac{\mu_0}{2}\times10^{-15}\]

• \[\mu_0\times10^{-15}\]

Answer 1

\[2\mu_0\times10^{-16}\]

Explanation:

A charged particle moving in a circular path acts like a current-carrying coil.

Let I be the current due to the particle current,

\[\mathrm{I=\frac{q}{t}=\frac{1000\times e}{1}=1000e}\]

Magnetic field at the centre due to a current-carrying coil,

\[\mathrm{B}_{\mathrm{centre}}=\frac{\mu_{0}}{4\pi}\frac{2\pi\mathrm{I}}{\mathrm{r}}=\frac{\mu_{0}}{4\pi}\frac{2\pi\times1000\mathrm{e}}{\mathrm{r}}\]

\[=\frac{\mu_0}{4}\frac{2\times1000\left(1.6\times10^{-19}\right)}{0.4}=2\mu_0\times10^{-16}\]