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

For the charge moving in the plane perpendicularly to the plane of magnetic field,
`Bqv=(mv^(2))/rrArrr=(mv)/(qB)" If "v_(1)=2v`,
and taking `B_(1)=B_(2)`
The radius of path `r_(1)=(2mv)/q^(B/2)=(4mv)/(qB)=4r`