Calculation of specific charge of an electron is one of the important theory of J.J. Thomson, which can be summarized as below.
J.J. Thomson takes the instrument where two different types of Pd are applied. First Pd applied to move the electron from filament and second to neutralize the electric field i.e. create a cross field, where electron can’t be deflected by electric field and magnetic field.
First when the (V) Pd applied then the electron moves with velocity (v);
I.e. ev= 1/2mv^2 where, V=required Pd to move the electron from filament to plate,
v=velocity of an electron,
The above equation becomes;
e/m=v^2/2V
In cross field,
eV1=Bev where, V1=Pd applied in cross field,
v1= velocity of an electron move in cross field,
Then above equation become;
v=V1/B
From above two equation;
Then;
e/m=V1^2/2B^2V
By this equation J.J. Thomson calculated the value of e/m is 1.8*1011cals/kg.
This value of e/m is applicable to calculate the value of mass of an electron.