# J.J. Thomson’s Experiment: Detailed Explanation

## J.J. Thomson’s Experiment Explanation

The experiment to determine the specific charge of the electron, commonly known as J.J Thomson’s Experiment, was performed by Joseph John Thomson in 1897, a professor of England. The specific charge of an electron is defined as the charge of electron per unit mass of it.

## Principle of Working (Cross fields)

J.J. Thomson used the principle of cross fields to determine the specific charge of an electron. If a uniform electric field and a uniform magnetic field are perpendicular in such a way that deflection produced by one on the charged particle is canceled by the deflection produced by another field, such fields are known as cross fields. The electric fields produced by the charged plates and the magnetic field produced by the circular coils carrying current can be an example of cross fields as shown in the figure.

The force on the charged particle due to the electric field is equal and opposite of the force on the charged particle due to the magnetic field.

Let ‘q’ be the charge carried by the charged particle moving with velocity ‘v’ in the electric field ‘E’ and magnetic field ‘B’. Then, we have

Force due to magnetic field (Fb) = Bqv and

Force due to electric field (Fe) = qE

Since we have, Fb = Fe

or, Bqv = qE

∴ v = E/B   ……..……… (1)

## Experimental Setup

The experimental setup for the J..J. Thomson’s experiment is as shown in the figure below. It consists of a highly evacuated discharge tube with a fluorescent screen coated with phosphorus. In the figure, F is the filament being heated by a small battery. The filament heats the cathode which emits a beam of an electron.

The electrons are then passed in between the cathode C and anode A which are connected to a very high voltage power supply up to 10kw. The beam of electrons is then subjected to cross fields, produced by two parallel plates connected to high voltage power supply and a coil carrying current.

The electric field and magnetic field are perpendicular to each other. The deflection produced by the electric field is upward and the deflection produced by the magnetic field is downward.

## Working of the device

When both the magnetic field and electric field are turned off, then the beam of an electron coming from the discharge tube passes straight, without any deviation, and strikes the fluorescent screen as a result a luminous spot appears at O.

When the magnetic field alone is applied, the beam of the electron is deflected downward and a luminous spot is seen at O”. Similarly, when the electric field alone is applied, then the beam of an electron is deflected upward and a luminous spot is seen at O’.

Now, if the electric and magnetic field both are applied simultaneously such that the ratio (E/B) is equal to the velocity (v) of the electrons. Then the beam of electron passes through the field without any deviation and a luminous spot is seen at O again.

Let ‘e’ be the charge and ‘m’ be the mass of an electron, ‘V’ be the potential difference between the cathode C and anode A and ‘v’ be the velocity with which the electrons enter into the field. Then, the kinetic energy gained by the electron is (1/2)mv2. This energy is provided by electrostatic potential energy eV.

Therefore, eV= (1/2) mv2………………. (2)