An electron and a proton enter region of uniform magnetic field in a direction at right angles to the field with the same kinetic energy. They describe circular paths of radius `r_(e)` and `r_(p)` respectively. Then

Options

A. `r_(e)=r_(p)`
B. `r_(e ) lt r_(p)`
C. `r_(e ) gt r_(p)`
D. `r_(e)` may be less than or greater than `r_(p)` depending on the direction of the magnetic field

Answer

B

Explanation

`r=(sqrt(2mK))/(qB)` i.e. `rprop (sqrt(m))/(q)`
Here Kintic energy `K` and `B` are same.
`:. (r_(e))/(r_(p)) =sqrt((m_(e))/(m_(p)))xx(q_(p))/(q_(e)) implies (r_(e))/(r_(p)) =sqrt((m_(e))/(m_(p)))( :'q_(e)=q_(p))`
Since `m_(e) lt m_(p)`, therefore `r_(e) lt r_(p)`