An electron and a proton are revolving along circular paths of equal radii and equal magnetic fields. Compare their kinetic energies.

Explanation

Magnitude of charge (e) of an electron and a proton are equal. The forc acting on a charge e travelling with a velocity v normal to a magnetic field of streight B is Bev. This force supplies the necessary centripetal force to revolve the charge along a circular path.
So, for the electron `(mv^(2))/(r)=Bev or, mv= Ber`
Similarly, for the proton MV=Ber
`:. mv=MV` (i.e., the momenta of both of the them are equal)
`:. ("kinetic energy of the electron")/("kinetic enery of the proton")`
`=((1)/(2)mv^(2))/((1)/(2)MV^(2))=((mv)^(2))/(m)*(M)/((MV)^(2))=(M)/(m)`
Since the mass of a proton (M) is about 1836 tiems that of an electron (m), the kinetic energy of the electron will be about 1836 times that of the proton.