An electron is accelerated from rest through a potential difference V. This electron experiences a force F in a uniform magnetic field. On increasing the potential difference to V', the force experienced by the electron in the same magnetic field becomes 2F. Then, the ratio `(V'//V)` is equal to

Options

A. `(4)/(1)`
B. `(2)/(1)`
C. `(1)/(2)`
D. `(1)/(4)`

Answer

A

Explanation

`K=(1)/(2)mv^(2)=eV or v-sqrt((2ev)/(m))`
Also `F=evB=e[sqrt((2eV)/(m))]xxB`
Therefore, `(F)/(2F)=sqrt((V_(1))/V_(2))=sqrt((V)/(V'))`
`:'(V')/(V)=(4)/(1)`