# J.J Thompson’s Experiment of Specific Charge

The ratio of charge to mass of an elementary particle is called the specific charge. The specific charge of the electron was first measured by JJ Thompson.

It is based on the principle that when a beam of electron is subjected to electric or magnetic field, it experiences force. By adjusting the magnitude and directions of the two fields, the net force on the electron is made zero. This is called cross field.

Thomson’s experiment for determination of specific charge

The apparatus consists of an evaluated chamber where electrons are produced by heating a filament ‘F’ by the low tension battery. The excited electrons are now accelerated by a high tension battery. The beam of electrons are forced by a metallic cap around filament which emerges out of a hole in anode as a fine beam. This beam of electrons when incidents on the screen produces spot‘s’ on the screen. There is a region where electric and magnetic field can be applied as required.

Since the electrons are accelerated by a voltage ‘V’ so the energy ‘eV’ gained by the electrons is converted to mechanical energy. This is given by:

$${eV = \frac{1}{2}m_ev^2}$$

$$\frac{e}{m_{e}} = \frac{v^2}{2V}…..(i)$$

The electric field E = V/d is applied, the upper plate being positive the electrons are deflected to s1 due to electric force Fe =eE. The magnetic field B is also applied on the same region such that electrons are opposite direction to that of electric force and in this case the spot is formed at s2 due to the magnetic force Fm =Bev.

At this condition,

Fe = Fm

Or, eE = Bev

Or, v =  E/V

Substituting this value in equation (i),

$$\frac{e}{m_{e}} = \frac{E^2}{2VB^{2}}…..(ii)$$

By measuring the values of E, V and B the specific charge of charge is determined and its value is 1.6×1011It has no unit.

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