ELECTROSTATICS A LEVEL

ELECTROSTATICS

Types of charge

An amber rod rubbed with dry wool for attracts small pieces of paper. A glass rod rubbed with  dry silk attracts small bits of paper. The rods are said to be electrified (to acquire charge) through the rubbing process.

Two amber rods rubbed with fur repel each other; similarly two glass rods rubbed with silk repel each other. An amber rod rubbed with fur attracts a glass rubbed with silk

The above observation show that:-

1. Unlike charges attract whereas like charges repel
2. There exist two types of charges

The charge that appears on a glass rod rubbed with silk has been labeled positive and that which appears on an amber rod rubbed with fur is negative.

Conservation charge

The algebraic sum of the electric charges in any closed system remains constant. Uncharged objects contain equal amounts of negative and positive charge. When a glass rod is rubbed with silk, negative charge is transferred from the glass rod to the silk, leaving the glass rod with equal and opposite charge. For the closed system consisting of a glass rod and silk, the algebraic sum of the electric charge is constant.

Electrons and atoms

An atom consists of a positively charged, sense nucleus, consisting of protons and neutron. Reading about the nucleus are the electrons. The charge of the electron is negative and equal to

Conductors, insulation and semi conductors

Atoms in solids are closely packed. The nuclei are separated by distances of 10^-10m. In conductors, most of the electrons  are bound to the parent nuclei but about one electron per atom is free to wander through the lattice  and can easily drift in one atom under an extreme electric field.

Insulators or di-electrics are materials in which all atomic electrons are bound to their potent nuclei. Electrons can be removed or added to an insulator only by expenditure of larger amounts of energy.

Semi conductors lie between conductors and insulators in their conduction properties. In semi conductors, a few electrons are free, the no of free electrons can be increased by heating.

THIS VIDEO EXPLAINS MORE ABOUT CONDUCTORS, SEMI CONDUCTORS AND INSULATORS

Charging by rubbing

When two unlike di-electric are rubbed together, heat is produced. The thermal energy is sufficiently to cause removal of the weakly bound electrons in one material. The former is left with net positive charge while the latter acquires net negative charge of equal magnitude as the positive charge.

Charge conservation

The total electric charge on any object is on integral multiple of electrons since the  charge is simply the algebraic sum of the charges of the elementary particles that make up the body. The charge on an elementary particle is either positive, zero or negative. Hence the charge scale equipments because the experiments involve a large number of electrons.

Charge detection

An electroscope can be used to detect charge. This consists of a metal rod A, to which a gold leaf or a very thin aluminum foil L is attached. The metal rod is fitted with a circular metal cup or disc B and is insulated from the metal casing C by means of a plug P.

The casing has glass or perpex windows through which the gold leaf may be observed.

The metal casing screens the gold leaf from external influences.

Suppose the electroscope is given negative charge by touching the cup with an amber rod previously rubbed with fur. The gold leaf discharges. If a boxy X of unknown charge is brought near the cup and an increased divergence is observed, then the charge on X is negative.

A decrease in divergence means that either X is neutral or it is positively charged. To distinguish between the two alternatives, the electroscope is discharged and then given positive charge X is then brought near the cap of the electroscope. An increase in divergence of the gold leaf implies that X is positively charged. A decrease in divergence means that X is neutral.

Electrostatic induction

Consider two identical metal spheres A and B supported by insulating stands suppose the spheres are brought into contact and a negatively charged rod is brought in the vicinity of A, positive charge is attracted towards the negatively charged rod and negative charge is repelled. If A and B are separated while the negatively charged rod still in place and the rod then removed tests show that A carries positive charge while B carried an equal amount of negative charge.

Charging by electrostatic induction

Suppose an amber rod R, rubbed with fur is brought near a conductor supported by an insulating stand as shown.

If the conductor is earthed when R is still in place, and then the rod removed, subsequent tests show that the conductor has acquired positive charge.

Explanation

Negative charge on the rod repels the loosely bound electron to the far side of the conducting sphere leaving charge on the near side. On earthing the sphere, electrons flow to the ground. When the earth is disconnected, the radial sphere left with positive charge. When the amber rod is withdrawn, the positive charge on the sphere distributes itself over the entire surface of the sphere.

THIS VIDEO EXPLAINS MORE ABOUT ELECTROSTATIC INDUCTION

 Faraday’s ice-pail experiment

The experiment reveals the manner in which charge is distributed on hollow conduction.

A metal sphere is suspended by an insulating thread is given positive charge. The sphere is then lowered into a metal can C connected to an uncharged electroscope as shown. The leaves of the electron are observed to diverge. The metal sphere is shiffed to various positions inside C but without touching C. the divergence θ on the electroscope is observed to remain the same.

The sphere is withdrawn from C. the leaf of the electroscope collapses. The sphere is again lowered into C. the leaf of the electroscope is observed to diverge by the same amounts as before.

The sphere is then allowed to touch the inner surface of the can. The divergence θ is observed to remain constant. The sphere is then withdrawn and tested for charge. It is found to have lost all its charge, showing that there must have been an equal negative charge on the inner surface of the can which neutralized the positive charge on the sphere.

Hence, when a charged body is enclosed by a hollow conductor, it induces on the inside of the conductor equal but opposite charge. The total charge inside a hollow conductor is always zero, either there are equal and opposite charges on the inside walls and than the volume (as was the case before Sphere touched the can) or there is no charge at all. Any net charge on a hollow conductor resides on the outside surface of the conductor.

THIS VIDEO EXPLAINS MORE ABOUT THE FARADAY’S ICE PAIL EXPERIMENT

Distribution of charge on the conductor

Consider a pear-shaped positively charged conductor held on an insulator stand.

To investigate the distribution of charge on the conductor, a proof plane used. This is a small metal disc on an insulating handle. When the proof plane is placed on the surface of the conductor, a sample charge is acquired by the proof plane. The plane is then transformed into a hollow can on electroscope and the deflection noted. The proof plane and electroscope are discharged. Samples of charge are picked from different parts of the conductor and in each case the deflection on the electroscope noted.

In this way it is discovered that the surface density of charge on an unsymmetrical conductor is greatest where the curvature is greatest, that is, where the radius of curvature is least.

In the figure, the distance of the dashed curve from the surface of the conductor is proportional to the density of charge on the surface.

There is high density of charge at the pointed end of the conductor using proof planes, one can also investigate the way charge is distributed on a hollow conductor.

Corona discharge

Consider a positively charged pointed particle in air. Because of high density of charge at pointed end, the electric field density there is very high. This causes air molecules near the sharp end to be ionized. Positive charges are repelled away from the sharp point while electrons are attracted into the conductor. Some of the charge on the conductor is neutralized. Thus the conductor loses some charge. It is though charge has leaked away. Below are two examples of corona discharge.

Applications of corona discharge

Lightening conductor

Lightening is rapid, high –current discharge between clouds or between a cloud and the ground. In the latter case, the large current when if passes through a building it can cause the building to burn down. Trees split up under the expansion of steam produced in the tree when the tree is struck by lightening. A lightening conductor is a sharp spiked conductor which is connected to a strip attached to a building and earthed.

Action: When a charged cloud passes over the conductor, opposite charge is induced on the conductor. A large electric field intensity exists at the pointed end which ionizes the air there.

The ions having charge similar to that on the cloud are repelled to the ground

The positive ions are attracted to the cloud and neutralize some of the negative charge on the cloud.

The Van der Graff Generator

Main features

It consists of a large hollow metal sphere S supported on an insulated tube T, A silk belt inside the tube is driven by an electric motor past a sharply pointed metal electrode, E₁ held at an electric potential of about 10⁴V relative to earth. As the belt moves upwards, it passes another sharply pointed metal electrode, E₂ connected on the inside of the hollow sphere.

Mode of operation

There is a high electric field intensity at the sharp ends E₁.

This ionizes the air there. The positive ions are repelled onto the belt. The positive charge is carried up by the belt towards the sphere it induces negative charge on the sharp ends E₂ and positive charge on the sphere to which the blunt end of E₂ is connected.

The high electric field held at the pointed ends of E₂ ionizes the air there, negative charges are repelled onto positive charge carried by the belt and neutralizes it before the belt passes over the upper pulley. This process of the belt charging up and discharging is repeated many times per second and each  time the belt passes, the sphere S charges up positively until the electric potential is about 10⁶V relative to earth. The electrical energy acquired comes from the work done by the motor to move the belt against a repulsion between positive charge on the sphere and positive charge on the belt.

THIS VIDEO EXPLAINS MORE ABOUT THE CORONA DISCHARGE

Coulombs law of electrostatics

The force between two charged bodies is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them.

 THIS VIDEO EXPLAINS MORE ABOUT THE COULOMBS LAW