Question

A beam of cathode rays is subjected to crossed Electric field $\left(E\right)$ and Magnetic field $\left(B\right)$. 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. $\frac{2V{E}^2}{B^2}$
• B. $\frac{2V{B}^2}{E^2}$
• C. $\frac{E^2}{2V{B}^2}$
• D. $\frac{B^2}{2E{V}^2}$

Answer 1

The correct option is C $\frac{E^2}{2V{B}^2}$

When a beam of cathode rays (or electrons) are subjected to crossed electric $\left(E\right)$ and magnetic $\left(B\right)$ fields and the beam is not deflected, we can say that the magnitude of the forces due to the electric and magnetic fields are equal.
i.e $BeV=eE$
$v=\frac{E}{B}\dots \left(1\right)$
If $V$ is the potential differnce between the anode and cathode, then,
$\frac{1}{2}m{v}^2=eV$
$\frac{e}{m}=\frac{v^2}{2V}\dots \left(2\right)$
Substituting the value of $v$ from equation (1) in equation (2), we get
$\frac{e}{m}=\frac{E^2}{2V{B}^2}$

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