An electron (mass m, charge -e), accelerated through a potential difference V, enters normally a uniform magnetic field B. What will be the radius of the circular motion of the electron ?

Explanation

If the electron is accelerated through a potential difference V, then kinetic energy gained by it,
`eV=(1)/(2)mv^(2)`
or `v= sqrt((2eV)/(m))`
Magnetic forece evB and centripetal force `=(mv^(2))/(r)`
So ` evB=(mv^(2))/(r)`
or, `r=(mv)/(eB)=(m)/(eB)=(m)/(eB) sqrt((2eV)/(m))=((2mV)/(2B^(2)))^(1//2)`