Question

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

• A. 2.25m
• B. 0.25m
• C. 13.0m
• D. 1.25m
• E. 3.25m

Answer 1

Answer: (D)

Given, $q=2\mu C=2\times {10}^{-6}C$
$f=6.25\times {10}^{12}Hz$
$B=6.28T$
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 $r=\frac{4\pi \times {10}^{-7}\times 2\times {10}^{-6}\times 6.25\times {10}^{12}}{6.28\times 2}$
$=1.25m$