Electrostatics[1]

 

The electromagnetic force between charged particles is one of the fundamental forces of nature.

Some bodies can be electrified (to become electrically charged) by an external influence (e.g. rubbing with other bodies). Thus, one can state that for some bodies there exists a separated characteristic named charge. One coulomb (C) is the unit of electric charge. There are two kinds of electric charges, which were given the names positive and negative. Like charges repel one another and unlike charges attract one another.

 

Electric charge is always conserved. That is, when one object is rubbed against another, charge is not created in the process. The electrified state is due to a transfer of charge from one object to the other. One object gains some amount of negative charge while the other gains an equal amount of positive charge. For example, when a glass rod is rubbed with silk, the silk obtains a negative charge that is equal in magnitude to the positive charge on the glass rod. We now know from our understanding of atomic structure that negatively charged electrons are transferred from the glass to the silk in the rubbing process. Similarly, when rubber is rubbed with fur, electrons are transferred from the fur to the rubber, giving the rubber a net negative charge and the fur a net positive charge. This process is consistent with the fact that neutral, uncharged matter contains as many positive charges (protons within atomic nuclei) as negative charges (electrons).

 

In 1909, Robert Millikan (18681953) discovered that electric charge always occurs as some integral multiple of a fundamental amount of charge e. In modern terms, the electric charge q is said to be quantized, where q is the standard symbol used for charge. That is, for electric charge we can write q=Ne where N is some integer. Other experiments in the same period showed that the electron has a charge -e and the proton has a charge of equal magnitude but opposite sign +e (e =1.602 10-19 C). Some particles, such as the neutron, have no charge. A neutral atom must contain as many protons as electrons. Because charge is a conserved quantity, the net charge in a closed region remains the same. If charged particles are created in some process, they are always created in pairs whose members have equal-magnitude charges of opposite sign.

 

All substances are classified in terms of their ability to conduct electric charge: Electrical conductors are materials in which electric charges move freely, whereas electrical insulators are materials in which electric charges cannot move freely.

Materials such as glass, rubber, and wood fall into the category of electrical insulators.

When such materials are charged by rubbing, only the area rubbed becomes charged, and the charge is unable to move to other regions of the material.

In contrast, materials such as copper, aluminum, and silver are good electrical conductors. When such materials are charged in some small region, the charge readily distributes itself over the entire surface of the material. If you hold a copper rod in your hand and rub it with wool or fur, it will not attract a small piece of

paper. This might suggest that a metal cannot be charged. However, if you attach a wooden handle to the rod and then hold it by that handle as you rub the rod, the rod will remain charged and attract the piece of paper. The explanation for this is as follows: Without the insulating wood, the electric charges produced by rubbing readily move from the copper through your body and into the Earth. The insulating wooden handle prevents the flow of charge into your hand. Semiconductors are a third class of materials, and their electrical properties are somewhere between those of insulators and those of conductors. Silicon and germanium are well-known examples of semiconductors commonly used in the fabrication of a variety of electronic devices, such as transistors and light-emitting diodes. The electrical properties of semiconductors can be changed over many orders of magnitude by the addition of controlled amounts of certain atoms to the materials.

 

 

 

Coulombs law is the fundamental law governing the force between any two charged particles.

Coulombs law states that electric force between two stationary charged particles

is inversely proportional to the square of the separation r between the particles and directed along the line joining them;

is proportional to the product of the charges q1 and q2 on the two particles;

is attractive if the charges are of opposite sign and repulsive if the charges have the same sign.

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Because the electric force obeys Newtons third law, the electric force exerted by q2 on q1 is equal in magnitude to the force exerted by q1 on q2 and in the opposite direction.

 

One can say that an electric field is associated with a charge and describe its effect on other charged particles.

An electric field is said to exist in the region of space around a charged object. When another charged object enters this electric field, an electric force acts on it.

The electric field E at a point in space is defined as the electric force Fe acting on a positive test charge q0 placed at that point divided by the magnitude of the test charge:

We say that an electric field exists at a point if a test charge at rest at that point experiences an electric force. Once the magnitude and direction of the electric field are known at some point, the electric force exerted on any charged particle placed at that point can be calculated from the above equation.

Furthermore, the electric field is said to exist at some point (even empty space) regardless of whether a test charge is located at that point.

 

To calculate the electric field at a point due to a group of point charges, we first calculate the electric field vectors at that point individually then add them vectorially. In other words, at any point, the total electric field due to a group of charges equals the vector sum of the electric fields of the individual charges (the superposition principle).

 

A convenient way of visualizing electric field patterns is to draw lines that follow the same direction as the electric field vector at any point. These lines, called electric field lines, are related to the electric field in any region of space in the following manner:

The electric field vector E is tangent to the electric field line at each point.

The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region. Thus, E is great when the field lines are close together and small when they are far apart.

The density of lines through surface A is greater than the density of lines through surface B. Therefore, the electric field is more intense on surface A than on surface B. Furthermore, the fact that the lines at different locations point in different directions indicates that the field is nonuniform.

 

Note that the lines become closer together as they approach the charge; this indicates that the strength of the field increases as we move toward the source charge.

The rules for drawing electric field lines are as follows:

The lines must begin on a positive charge and terminate on a negative charge.

The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge.

No two field lines can cross.

 

Electric potential

When the test charge is moved in the field by some external agent, the work done by the field on the charge is equal to the negative of the work done by the external agent causing the displacement. When the test charge is moved in the field by some external agent, the work done by the field on the charge is equal to the negative of the work done by the external agent causing the displacement. As this amount of work is done by the field, the potential energy of the chargefield system is decreased by an amount For a finite displacement of the charge from a point A to a point B, the change in potential energy of the system is

or


The potential energy per unit charge U/q0 is independent of the value of q0 and has a unique value at every point in an electric field. This quantity U/q0 is called the electric potential (or simply the potential) V. Thus, the electric potential at any point in an electric field is

The potential difference between any two points A and B in an electric field is defined as the change in potential energy of the system divided by the test charge q0

 

The potential difference is proportional to the change in potential energy, and two are related by

Because electric potential is a measure of potential energy per unit charge, the SI unit of both electric potential and potential difference is joules per coulomb, which is defined as a volt (V):

 

An equipotential surface is one on which all points are at the same electric potential. Equipotential surfaces are perpendicular to electric field lines.

 

The electric potential due to a point charge at any distance r from the charge is

 

The potential energy associated with a pair of point charges separated by a distance

This energy represents the work required to bring the charges from an infinite

separation to the separation r12.

 

A capacitor consists of two conductors carrying charges of equal magnitude but

opposite sign. The capacitance C of any capacitor is the ratio of the charge Q on

either conductor to the potential difference DV between them:

 

The SI unit of capacitance is coulombs per volt, or the farad (F).

 

Work is required to charge a capacitor because the charging process is equivalent to the transfer of charges from one conductor at a lower electric potential to another conductor at a higher potential.

In dielectric media the external electric field is reduced. The decrease in the magnitude of E arises from an internal electric field produced by aligned dipoles in the dielectric. This internal field produced by the dipoles opposes the applied field due to the capacitor plates, and the result is a reduction in the net electric field.

 

 



[1] In this lecture we closely follow one of the best textbooks, Fundamentals of Physics by D. Halliday, R. Resnick, and J. Walker