A beam of cathode rays is subjected to crossed electric ( $E$ ) and magnetic fields ( $B$ ). The fie

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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)\

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(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 magnetic field = Force on electron due to electric field $$ B e v=e E 	ext { or } v=\frac{E}{B} 	ag{i} $$ If $V$ is the potential difference between the anode and the cathode, then $$ \frac{1}{2} m v^{2}=e V \quad 	ext { or } \quad \frac{e}{m}=\frac{v^{2}}{2 V} 	ag{ii} $$ 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 $\frac{e}{m}=\frac{E^{2}}{2 V B^{2}}$\