Question

A beam of cathode rays is subjected to crossed electric (E) and magnetic fields (B). The fields are adjusted such that the beam is not deflected.The specific charge of the cathode rays is given by

(Where V is the potential difference between cathode and anode)

Answer 1

The correct option is (d).

Explanation:

When a beam of cathode rays (or electrons) are subjected to crossed electric (E) and magnetic (B) fields, the beam is not deflected, if 

Force on electron due to = Force on electron due magnetic field to electric field

Bev = eE

or v = E/B  .......(i)

If V is the potential difference between the anode and the cathode, then

1/2mv² = eV

e/m = v²/2V .......(ii)

Substituting tire value of rt from equation (i) in equation (ii), we get

e/m = E²/2VB²

Specific charge of the cathode rays e/m = E²/2VB²