Electrostatics of Conductor
1. Net electric field intensity in the interior of a conductor is zero.
When a conductor is placed in an electrostatic field, the charges (free electrons) drift towards the positive plate leaving the +ve core behind. At equilibrium, the electric field due to the polarisation becomes equal to the applied field. So, the net electrostatic field inside the conductor is zero.
2. The electric field just outside the charged conductor is perpendicular to the surface of the conductor
Suppose the electric field is acting at an angle other than 90°, then there will be a component E cosθ acting along the tangent at that point to the surface which will tend to accelerate the charge on the surface leading to ‘surface current’. But there is no surface current in electrostatics. So, θ=90°and cos90°=0.
3. Net charge in the interior of a conductor is zero.
The charges are temporarily separated. The total charge of the system is zero.
Since E = 0 in the conductor's interior, therefore q = 0.
4. Charge always resides on the surface of a conductor.
Suppose a conductor is given some excess charge q. Construct a Gaussian surface just inside the conductor. Since E = 0 in the conductor's interior, q = 0 inside the conductor.
5. Electric potential is constant for the entire conductor.
We have,
dV = - E . dr
Since E = 0 in the interior of the conductor, therefore
dV = 0.
i.e. V = constant.
6. Surface charge distribution may be different at different points.
We have,
surface charge density,
σ = q /s
Every conductor is an equipotential volume (three-dimensional) rather than just an equipotential surface (two-dimensional)
7. Electrostatics Shielding
It is the process of isolating a certain region of space from an external field. It is based on the fact that the electric field inside a conductor is zero. A conductor has a cavity with no charge inside the cavity, then no matter what happens outside the conductor. Even if there are intense electric fields outside the conductor, the cavity inside has, shielding whatever is inside the cavity from whatever is outside the cavity. This is called electrostatic shielding.
8. DIELECTRICS AND POLARIZATION:
Polar Molecules:
A molecule in which the center of positive charges does not coincide with the center of negative charges is called a polar molecule. The polar molecule does not have a symmetrical shape. Eg. HCl, H2O, NH3 , CO2, alcohol, etc.
Effect of Electric Field on Polar Molecules:
In the absence of an external electric field, the permanent dipoles of the molecules orient in random directions and hence the net dipole moment is zero.
When an electric field is applied, the dipoles orient themselves in a regular fashion and hence dipole moment is induced. Complete alignment is not possible due to thermal agitation.
Non-polar Molecules:
A molecule in which the center of positive charges coincides with the center of negative charges is called a non-polar molecule. A non-polar molecule has a symmetrical shape. Eg. N2, CH4, O2 , C6H6 , etc.
Effect of Electric Field on Non-polar Molecules:
In the absence of an external electric field, the effective positive and negative centers coincide and hence dipole is not formed.
When an electric field is applied, the positive charges are pushed in the direction of the electric field and the electrons are pulled in the direction opposite to the electric field. Due to the separation of effective centers of positive and negative charges, dipole is formed.
Dielectrics:
Generally, a non-conducting medium or insulator is called a ‘dielectric’. Precisely, the non-conducting materials in which induced charges are produced on their faces on the application of electric fields are called dielectrics. Eg. Air, H2, glass, mica, paraffin wax, transformer oil, etc.
Polarization of Dielectrics:
When a non-polar dielectric slab is subjected to an electric field, dipoles are induced due to the separation of effective positive and negative centers. E0 is the applied field and Ep is the induced field in the dielectric.
The net field is EN= E0 – Ep i.e. the field is reduced when a dielectric slab is introduced.
The dielectric constant is given by
Polarization Vector:
The polarization vector measures the degree of polarization of the dielectric. It is defined as the dipole moment of the unit volume of the polarized dielectric. If n is the number of atoms or molecules per unit volume of the dielectric, then the polarization vector is
SI unit of polarization vector is Cm-2.
Dielectric Strength:
Dielectric strength is the maximum value of the electric field intensity that can be applied to the dielectric without its electric breakdown. Its SI unit is Vm-1.
9. Van De Graaff Generator:
Principle:
Consider two charged conducting spherical shells such that one is smaller and the other is larger. When the smaller one is kept inside the larger one and connected together, the charge from the smaller one is transferred to the larger shell irrespective of the higher potential of the larger shell. i.e. The charge resides on the outer surface of the outer shell and the potential of the outer shell increases considerably.
Sharp pointed surfaces of a conductor have large surface charge densities and hence the electric field created by them is very high compared to the dielectric strength of the dielectric (air).
Therefore air surrounding these conductors gets ionized and the like charges are repelled by the charged pointed conductors causing a discharging action known as Corona Discharge or Action of Points. The sprayed charges moving at high speed cause electric wind.
Opposite charges are induced on the teeth of the collecting comb (conductor) and again opposite charges are induced on the outer surface of the collecting sphere.
Construction:
Van de Graaff Generator consists of a large (about a few meters in radius) copper spherical shell (S) supported on an insulating stand (IS) which is several meters high above the ground. A belt made of insulating fabric (silk, rubber, etc.) is made to run over the pulleys (P1, P2 ) operated by an electric motor (M) such that it ascends on the side of the combs. Comb (C1) near the lower pulley is connected to a High Voltage Rectifier (HVR) whose other end is earthed. Comb (C2) near the upper pulley is connected to the sphere S through a conducting rod. A tube (T) with the charged particles to be accelerated at its top and the target at the bottom is placed as shown in the figure. The bottom end of the tube is earthed to maintain lower potential. To avoid the leakage of charges from the sphere, the generator is enclosed in a steel tank filled with air or nitrogen at very high pressure (15 atmospheres).
Working:
Let the positive terminal of the High Voltage Rectifier (HVR) be connected to the comb (C1). Due to the action of points, electric wind is caused and the positive charges are sprayed onto the belt (silk or rubber). The belt made ascending by electric motor (EM) and pulley (P1) carries these charges in the upward direction.
The comb (C2) is induced with the negative charges which are carried by conduction to the inner surface of the collecting sphere (dome) S through a metallic wire which in turn induces positive charges on the outer surface of the dome.
The comb (C25) being negatively charged causes electric wind by spraying negative charges due to the action of points which neutralize the positive charges on the belt. Therefore the belt does not carry any charge back while descending. (Thus the principle of conservation of charge is obeyed.)
The process continues for a longer time to store more and more charges on the sphere and the potential of the sphere increases considerably. When the charge on the sphere is very high, the leakage of charges due to ionization of surrounding air also increases. Maximum potential occurs when the rate of charge carried in by the belt is equal to the rate at which charge leaks from the shell due to the ionization of air.
Now, if the positively charged particles which are to be accelerated are kept at the top of the tube T, they get accelerated due to a difference in potential (the lower end of the tube is connected to the earth and hence at the lower potential) and are made to hit the target for causing nuclear reactions, etc.
10. Uses of Van De Graaff Generator:
- Van de Graaff Generator is used to produce very high potential difference (of the order of several million volts) for accelerating charged particles.
- The beam of accelerated charged particles is used to trigger nuclear reactions.
- The beam is used to break atoms for various experiments in Physics.
- In medicine, such beams are used to treat cancer.
- It is used for research purposes.
✍️ Dibya Jyoti Deka, M.Sc., B.Ed. (Lecturer of Physics)
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