An electron of mass `m` and charge `q` is travelling with a speed `v` along a circular path of radius `r` at right angles to a uniform of magnetic field `B`. If speed of the electron is doubled and the magnetic field is halved, then resulting path would have a radius of

Options

A. r/4
B. r/2
C. 2r
D. 4r

Answer

D

Explanation

`r = (mv)/(qB) implies r prop (v)/(B)`
`(r_(1))/(r_(2)) = ((v_(1))/(v_(2))) ((B_(2))/(B_(1))) = ((1)/(2)) ((1)/(2)) implies r_(2) = 4r_(1) ` i.e. 4r