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

$Be\upsilon = eE$

or $\quad v=\frac{E}{B}$     …… $(i)$

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

${\frac{1}{2} m v^{2}=e V}$

${\frac{e}{m}=\frac{v^{2}}{2 V}}$   ….. $(ii)$

Substituting the value of $v$ from equation $(i)$ in equation $(ii)$, we get

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

Specific charge of the cathode rays $\frac{e}{m}=\frac{E^{2}}{2 V B^{2}}$