A beam of cathode rays is subjected to crossed electric and . . .

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 

a) B²/2VE²

b) 2VB²/E²

c) 2VE²/2B²

d) E²/2VB²

where V is the potential difference between cathode and anode.

Doubt by Jayant

Ans : d) would be the correct answer.

Solution : We know
½mv² =qV

v² = 2qV/m

For electron (e)

q = e
v² = 2eV/m

for undeflected beam, v=E/B

(E/B)² = 2eV/m
E²/B² = 2eV/m

E²/2VB² = e/m

Hence,

Specific Charges (e/m)  = E²/2VB²

Hence, d) would be the correct answer.