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  4. A 2μ C charge moving around a circle with a frequency of 6.25× 1012Hz produces a magnetic field 6.28 T at the centre of the circle. The radius of the circle is

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Q. 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

KEAMKEAM 2010Moving Charges and Magnetism

Solution:

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 $