IIT JEE Physics Formula Revision 41. Electric Current through Gases

1. Paschen's law
Sparking potential of a gas in a discharge tube is a function of the product of the pressure of the gas and the separation between the electrodes.

V = f(pd)


2. Experiment to Determine e/m by Thomson

Cathode rays are subjected to electric and magnetic fields.

If both the electric field and magnetic field are switched on and the values are so chosen that

v = E/B

The magnetic field evB will exactly cancel the electric force eE and the beam will pass undeflected. If the potential difference between the anode and the cathode is V, the speed of the electrons coming out of A is given by

½ mv² = eV

as v = E/B

½ m (e/B) ² = eV
therefore e/m = E²/2B²V


3. If n thermions are ejected per unit time by a metal surface, the thermionic current i = ne. This current is given by the Richardson-Dushman equation.

i = ne = AST²e^{- φ/kT}

where
S = surface area
T = the absolute temperature of the surface.
φ = work function of the metal
K = Boltzmann constant
A = constant which depends only the nature of the metal