A electron `e^(-)` is accelerated by V volts experiences a force F, when it enters in a uniform magnetic field. What will the force experienced when it is accelerated by 2V?

Options

A. `sqrt(2)F`
B. F
C. 2F
D. `F/2`

Answer

A

Explanation

When `e^(-1)` is accelerated by V volts, then work doen by `e^(-)` is equals to kinetic energy of `e^(-)`.
or `qV= 1/2 mv^(2)`
Then, the velocity of `e^(-1)` is `v= sqrt((2qV)/m)`
or `v=ksqrt(V)`.
When `e^(-)` accelerated by V volts, then `v=ksqrt(V)`.
Force experienced by `e^(-)` in a uniform magnetic field, `F=qvB`
or `F=qksqrt(v)B`.......(i)
`therefore F_(1)=qv_(1)B=qksqrt(2V)B`
Hence, `F_(1) = sqrt(2)F` from Eq. (i)