A charged particle is accelerated through a potential difference of 12 kV and acquires a speed of ${10}^6$ m/s. It is then injected perpendicularly into a magnetic field of strength 0.2T. Find the radius of circle described by it

Given data

Potential difference $=12 kV=12000 v$

Speed=${10}^6$ m/s.

Magnetic field $B=0.2 T$

Concepts used moving charges and magnetism

Explanation

By equating centripetal force and electron force 

$\frac{m{v}^2}{2}=qV$

$\frac{q}{m}=\frac{v^2}{2V}=\frac{{10}^{12}}{2\times 12\times {10}^3}=\frac{{10}^9}{24}$

$r=\frac{mv}{qB}$

$r=\frac{24}{{10}^9}\frac{{10}^6}{0.2}=12 cm$