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 (Where $V$ is the potential difference between cathode and anode)

• A. $\frac {B^2}{2VE^2}$
• B. $\frac {2VB^2}{E^2}$
• C. $\frac {2VE^2}{B^2}$
• D. $\frac {E^2}{2VB^2}$

Answer 1

Answer: (D)

$\frac {E^2}{2VB^2}$

Answer 2

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 Bev = eE
or $v= \frac {E}{B}...(i)$
If $V$ is the potential difference between the anode and the cathode, then
$\therefore \frac {1}{2}mv^2=eV$
$\frac {e}{m}= \frac {v^2}{2V} ...(ii)$
Substituting the value of $v$ from equation (i) in equation (ii), we get
$\frac {e}{m}= \frac {E^2}{2VB^2}$
Specific charge of the cathode rays $\frac {e}{m}= \frac {E^2}{2VB^2}$