Question

A $2\mu C$ charge moving around a circle with a frequency of $6.25\times {{10}^{12}}Hz$ produces a magnetic field $6.28\, T$ at the centre of the circle. The radius of the circle is

• A. 2.25m
• B. 0.25m
• C. 13.0m
• D. 1.25m

Answer 1

Answer: (D)

1.25m

Answer 2

Given, $q=2\mu C=2\times {{10}^{-6}}C$
$f=6.25\times {{10}^{12}}Hz$
$B=6.28\text{ }T$
The magnetic field at the centre of the circle
$B=\frac{{{\mu }_{0}}i}{2r}=\frac{{{\mu }_{0}}qf}{2r}$
$[\because i=qf]$
$6.28=\frac{4\pi \times {{10}^{-7}}\times 2\times {{10}^{-6}}\times 6.25\times {{10}^{12}}}{2r}$
or $r=\frac{4\pi \times {{10}^{-7}}\times 2\times {{10}^{-6}}\times 6.25\times {{10}^{12}}}{6.28\times 2}$
$=1.25m$