d
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 \(\frac{e}{m}=\frac{E^{2}}{2 V B^{2}}\)