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., r prop (sqrt(m))/(q)`
Here kinetic energy `K` and `B` are same
`:. (r_(e))/(r_(p)) = sqrt((m_(e))/(m_(p))) xx (q_(p))/(q_(e))`
`implies (e_(e))/(r_(p)) = sqrt((m_(e))/(m_(p))) ( :' q_(e) = q_(p))`
Since `m_(e) lt m_(p)`, therefore `r_(e) lt r_(p)`