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Electrostatic Potential Energy Expression

We shall do some work in bringing the two charges to a certain separation against the electric force of repulsion between them. Once after this work is done, energy used for this purpose cannot disappear. It will convert into electrostatic potential energy between that charged particles and hence conservation of energy concept is satisfied.

Let us consider two charges separated by a certain distance. Between them there is certain potential energy. We can define work done as the product of potential difference between the charges and charge that is brought towards the other charge. Once the job is done this work done is actually stored in the form of electrostatic potential energy.

We can derive an expression for electrostatic potential energy of a charged particle placed on the surface of a sphere as shown in the diagram below.

It can be noticed that we shall do work in bringing each charge to that particular location and we shall do the work for that. All that work done is stored in the form of potential energy. The same is the case with four charges placed at the four corners of a square as shown below.

If three charges are to be placed at the three corners of a triangle, we need to do some work and that work is stored in the form of potential energy. We can write the expression for it as shown in the diagram below.

We can even a small problem about the case of triangle with the solution as shown below.

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Millikan Oil Drop Method to determine Charge of Electron

We can calculate the charge on the electron basing on Millikan’s oil drop experiment. Between the two circular identical plates oil drops are sprinkled through a device called atomizer. The purpose of this device is to produce very small oil drops.

On the oil drop there are multiple forces acting. Weight is the force that is always acting in the downward direction, up thrust is the force that always acts in the upward direction. When the drop starts moving, there is another force called viscous force starts acting against the motion.

Viscous force is similar to frictional force which opposes the relative motion. As the drop starts moving in the downward direction, viscous force also increases in the upward direction. Being the downward force is constant and the upward force is steadily increasing, at a particular stage these two forces are going to be balanced with each other. At that instant the drop acquires a constant velocity and the velocity is called as terminal velocity.

The oil drops during the motion acquires a positive charge due to friction. If a electric field is applied in the upward direction, the drops starts experiencing a new electric force in the upward direction.

Again at the equilibrium state, the drop will acquire a different terminal velocity and by combining both the cases we can derive the equation for the charge.

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Determination of Specific Charge of Electron J J Thomson Experiment

The entire subject of physics can be broadly divided into two categories like classical physics and the modern physics. Classical physics deals with the macroscopic objects which moves with the velocity that is very much smaller than the velocity of light. Modern physics deals with objects which are microscopic in nature and moves with the velocity comparable to the velocity of light.

As per the concepts of modern physics, both radiation and matter has dual nature. The travel like a wave and it interacts like a particle. Discovery of the cathode rays is one of the important starting points of modern physics.

In a discharge tube if a very low pressure of 0.01 mm of Hg and a high voltage of 10,000 V is applied, invisible cathode rays are generated. These rays are invisible and they start from the cathode. They are nothing but stream of electrons which travel in straight lines with high velocity which is equal to 1 by 10^th of velocity of light.

As they are having some velocity, they possess kinetic energy. They effect photographic plates and they can ionize the gases. As they are having a negative charge, they are affected by both electric and magnetic fields. The cathode rays are independent of the medium that is present in the discharge tube.

We can determine the specific charge of the cathode rays using JJ Thomson experiment. The apparatus consists of a discharge tube where a low pressure and high voltage is applied. There is a provision to apply electric and magnetic fields perpendicular to each other within the discharge tube. The cathode rays are allowed to strike a surface made up of zinc surface. When the invisible cathode Ray strikes the surface, there will be scintillation formed on the screen. Basing on the location of the scintillation we can identify the path of the cathode ray .

When no electric and magnetic fields are applied, cathode Ray travels along a straight line and strikes the screen exactly on the middle of the screen. When electric field is applied, there is a force acting on the cathode is therefore they were attracted towards the positive plate of the battery and hence modify their path.

When only magnetic field is applied perpendicular to previous electric field, the cathode Ray takes circular path. If both electric and magnetic fields are applied simultaneously in such a way that they apply equal force on the cathode ray, the cathode Ray goes in a undeviated manner.

We can derive the equations for specific charge basing on the equations of force experienced by the charged particle when electric field alone is applied and one magnetic field alone is applied.

When both the fields are applied perpendicular to each other, and if they are magnitudes are equal in size, the cathode Ray goes in a undeviated manner. It means that the cathode ray electron is in equilibrium position and hence we can equate both the forces.

When the cathode Ray is released, it is because of the high-voltage that is applied. Hence it will acquire some potential energy and by the time the cathode ray reaches the screen, all this potential energy is converted into kinetic energy. By applying the law of conservation of energy we can equate both these energies and derive an equation further for specific charge as shown below.