When a magnetic field is applied in a direction perpendicular to the direction of cathode rays,then their

$A$ cathode emits $1.8 \times 10^{14}$ electrons per second when heated. When $400 \ V$ is applied to the anode,all the emitted electrons reach the anode. The charge on an electron is $1.6 \times 10^{-19} \ C$. The maximum anode current is ............ $\mu A$.

The relation between current and charge is given by $I = A T^2 e^{qV / V_L}$. What is the value of $V_L$?

$A$ 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):

$(a)$ Estimate the speed with which electrons emitted from a heated emitter of an evacuated tube impinge on the collector maintained at a potential difference of $500\;V$ with respect to the emitter. Ignore the small initial speeds of the electrons. The specific charge of the electron,$i.e.$,the $e/m$ is given to be $1.76 \times 10^{11}\; C\; kg^{-1}$.
$(b)$ Use the same formula you employ in $(a)$ to obtain electron speed for a collector potential of $10\;MV$. Do you see what is wrong? In what way is the formula to be modified?

Cathode rays are similar to visible light rays in that