Question

A particle having charge $10$ times that of the electron revolves in a circular path of radius $0.4m$ with an angular speed of one rotation per second. The magnetic induction produced at the centre of the circular path is:

• A. $4\pi \times {10}^{-26}T$
• B. $2\pi \times {10}^{-26}T$
• C. $16\pi \times {10}^{-26}T$
• D. $8\pi \times {10}^{-25}T$
• E. $9\pi \times {10}^{-25}T$

Answer 1

The correct option is D $8\pi \times {10}^{-25}T$

Given, charge $q=10$e
Radius, $r=0.4$m
$e=1.6\times {10}^{-19}C$
The magnetic induction produced at the centre of the coil
$B=\frac{{\mu }_{0}I}{2r}$
${\mu }_0=4\pi \times {10}^{-7}$MKS units
$B=\frac{4\pi \times {10}^{-7}\times 10e}{2\times 0.4\times 1}$ $[\because I=\frac{q}{t}=\frac{10e}{1}]$
$=\frac{4\pi \times {10}^{-7}\times 10\times 16\times {10}^{-19}}{0.8}$
$=8\pi \times {10}^{-25}$T.