An `(alpha)`-particle and a proton are both simultaneously projected in opposite direction into a region of constant magnetic field perpendicular to the direction of the field. After some time it is found that the velocity of the `(alpha)`-particle has changed in a direction by `45^(@)`. Then at this time, the angle between velocity vectors of `(alpha)`-particle and proton is

Options

A. `90^(@)`
B. `45^(@)`
C. `135^(@)`
D. none

Answer

C

Explanation

`omega=qB//m, omega_(p)=eB//m, omega_(alpha)=(2eB)/(4m)=2omega_(p)`

So proton will cover double angle in same time a that of `alpha`-particle. Clearly from figure angle between `v_(alpha)` and `v_(p)` is `135^(@)`.