Question

An electron and a proton are moving with the same kinetic energy along the same direction . When they pass through a uniform magnetic field perpendicular to the direction of their motion , they describe circular paths of the same radius.

Answer 1

when a charged particle passes through a uniform magnetic field perpendicular to the direction of motion , a force acts as a centripetal force
`:. (mv^(2))/ ( r ) = q^(vB)`
` r = (sqrt(2mk))/(q^(B) [ where K = (p^(2))/(2m)] `
:. ` r prop (sqrt(m))/(q) ` [ for const. K.E. and B]
Here , `q` is same for electron and proton
:. ` r prop sqrt(m)`
Radius of proton will be more.