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. $\frac{B^2}{2v{E}^2}$
• B. $\frac{2v{B}^2}{E^2}$
• C. $\frac{2v{E}^2}{B^2}$
• D. $\frac{E^2}{2v{B}^2}$

Answer 1

The correct option is D $\frac{E^2}{2v{B}^2}$

Its the electron beam is not deflected then,

$F_m=Ee$

$Bev=Ee$

$v=\frac{E}{B}$

According to the law of conservation of energy

$\frac{1}{2}m{v}^2=eV$

$v=\sqrt{\frac{2eV}{m}}$

$\sqrt{\frac{2eV}{m}}=\frac{E}{B}$

$\frac{e}{m}=\frac{E^2}{2V{B}^2}$