1.2 Electrostatic: Coulomb's Law

Coulombs's Law

Coulomb measured the magnitudes of the electric forces between charged objects using the torsion balance. Coulomb’s experiments showed that the 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.

From these observations, we can express Coulomb’s law as an equation giving the magnitude of the electric force (sometimes called the Coulomb force) between two point charges:

where ke is a constant called the Coulomb constant. In his experiments, Coulomb was able to show that the value of the exponent of r was 2 to within an uncertainty of a few percent. Modern experiments have shown that the exponent is 2 to within an uncertainty of a few parts in 1016. The value of the Coulomb constant depends on the choice of units. The SI unit of charge is the coulomb (C). The Coulomb constant ke in SI units has the value

where the constant (epsilon) is known as the permittivity of free space.

When dealing with Coulomb’s law, you must remember that force is a vector quantity and must be treated accordingly. Thus, the law expressed in vector form for the electric force exerted by a charge q1 on a second charge q2 , written F12 , is

where is a unit vector directed from q1 to q2 ,

Because the electric force obeys Newton’s 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.

1.1 ELECTROSTATIC

Contents

1) Concept of  Electrical Charges 
2) Conductor and Insulator

3) Coulombs's law

4) Superposition principle

6) Electric Field

7) Electric Dipole and its  electric field

8) Torque on dipole in Uniform Electric field

9) Motion of Charged Particles in a Uniform Electric field

10) Electric Field Lines

11) Electric Flux

12) Gauss's Law and its application

13) Electrostatic Potential

14) Capacitance  

Electrostatics is the branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges with no acceleration.

in this chapter we will discuss the properties of electric charge, force applied by them and field created by them.we will also see the answer of some questions like 

How can an object be charged?

What affect does that charge have upon other objects? 

Concept of charge

atoms are the building blocks of matter and we have studied about atoms in atomic structure of chemistry classes that

1) All material objects are composed of atoms. There are different kinds of atoms known as elements; these elements can combine to form compounds. Different compounds have distinctly different properties.

2) An atom consists of a nucleus and a vast region of space outside the nucleus. Electrons are present in the region of space outside the nucleus, They are negatively charged and weakly bound to the atom. Electrons are often removed from and added to an atom by normal everyday occurrences. These occurrences are the focus of this Static Electricity.

3) The nucleus of the atom contains positively charged protons and neutral neutrons. These protons and neutrons are not removable by usual everyday methods (it may be possible in nuclear reaction and reactor) thus protons and neutrons will remain within the nucleus of the atom, so Electrostatic phenomenon can never be explained by the movement of protons.

The number of electrons that surround the nucleus will determine whether or not an atom is electrically charged or electrically neutral. The amount of charge on a single proton is equal to the amount of charge possessed by a single electron. A proton and an electron have an equal amount but an opposite type of charge. Thus,

1) if an atom contains equal numbers of protons and electrons, the atom is described as being electrically neutral.

2) if an atom has an unequal number of protons and electrons, then the atom is electrically charged (and in fact, is then referred to as an ion rather than an atom). 

Any particle, whether an atom, molecule or ion, that contains less electrons than protons is said to be positively charged. 

Conversely, any particle that contains more electrons than protons is said to be negatively charged.

 thus we can simply say that charged object as an imbalance of protons and electrons.

Properties of Charge

1) Charge with same electrical sign repel each other, and charge with opposite electrical signs attract each other.

Interaction Between Charged and Neutral Objects

The interaction between two like-charged objects is repulsive. The interaction between two oppositely charged objects is attractive. 
What type of interaction is observed between a charged object and a neutral object? 
The answer is quite surprising to many students of physics. Any charged object - whether positively charged or negatively charged - will have an attractive interaction with a neutral object. Positively charged objects and neutral objects attract each other; and negatively charged objects and neutral objects attract each other.


This third interaction between charged and neutral objects is often demonstrated as, if a charged balloon is held above neutral bits of paper, the force of attraction for the paper bits will be strong enough to overwhelm the downward force of gravity and raise the bits of paper off the table. If a charged plastic tube is held above some bits of paper, the tube will exert an attractive influence upon the paper to raise it off the table. Any charged object - plastic, rubber, or aluminum - will exert an attractive force upon a neutral object. And in accordance with Newton's law of action-reaction, the neutral object attracts the charged object.

Because charged objects interact with their surroundings, an observed interaction provides possible evidence that an object is charged. Suppose that two balloons suspended from the ceiling, Rather than hanging straight down vertically, the balloons are hanging at an angle, exhibiting a repulsive interaction.
The only way that two objects can repel each other is if they are both charged with the same type of charge. Thus, the repulsion of the balloons provides conclusive evidence that both balloons are charged and charged with the same type of charge. One could not conclude that the balloons are both positively charged or both negatively charged. Additional information or further testing would be required to make a conclusion about the type of excess charge present upon the balloons. Nonetheless, one can be convinced that both balloons possess an excess charge - either positive or negative.

Suppose that two balloons suspended from the ceiling and exhibiting an attractive interaction. There are two underlying reasons for two objects attracting each other. One balloon could be neutral and the other balloon charged or both balloons could be charged with the opposite type of charge. Thus, your only conclusion could be that at least one of the balloons is charged. The other balloon is either neutral or charged with the opposite type of charge. You cannot draw a conclusion about which one of the balloons is charged or what type of charge (positive or negative) the charged balloon possesses. Additional information or further testing would be required to make these conclusions. For example, if you could take each balloon and individually bring them near some neutral bits of paper, you could test to see if each individual balloon is charged or neutral. If a balloon were charged, then it would exhibit an attractive interaction with the neutral paper bits. On the other hand, an uncharged balloon would not interact at all with neutral paper bits.

The above thought experiments illustrate the conclusive nature of a repulsive interaction. When objects repel each other, one can be certain that both objects are charged same. On the other had, the observation of an attractive interaction leads to limited conclusions. At best, one can conclude that at least one of the objects is charged.

In all likelihood, most of us have only heard of two types of charge interactions (opposites attract and likes repel); and both of these charge interactions are fundamental interactions. The third statement - any charged object and a neutral object will attract each other - is simply an observable fact that can be explained by the two fundamental charge interactions. 

2) Quantization of Charge

Like mass, the charge of an object is a measurable quantity. The charge possessed by an object is often expressed using the scientific unit known as the Coulomb. Coulomb of charge is an abnormally large quantity of charge, so the units of microCoulombs (µC) or nanoCoulombs (nC) are more commonly used as the unit of measurement of charge.

The charge on a single electron (e) is =  -1.6 x 10 ^-19 Coulomb.

we have already studied that charged is developed by the transfer of electron (imbalance of protons and electrons) and electrons transfer is in integer (n = 1, 2, 3, 4 ......)

so mathematically charge on a body is always express as q = ne

this occurrence of charges in discrete units is called quantization of charge.

so quantization of charge means the body will have charge value in the form of (q =  ne) and never a fraction of e (-1.6 x 10 ^-19 Coulomb).

3) Conservation of charge

charge is the transfer of electrons from one body to another body, charge is neither created nor be destroyed it only transfer from one body to another body.  

it is found that in all interaction in nature, the total charge of an isolated system remains constant this is called conservation of charge.

4) Charge is a scalar quantity because its add algebraically. 

5) Charge can not exist without mass.

6) Charge is transferable.

7) Charge on a body is not change with its speed (mass and length of body change with speed as in relativity).  

8) It follows Newtons third law of of motion.

Method of Charging

1) Charging by friction

The frictional charging process results in a transfer of electrons between the two objects that are rubbed together. Rubber has a much greater attraction for electrons than animal fur(hair). As a result, the atoms of rubber pull electrons from the atoms of animal fur, leaving both objects with an imbalance of charge. The rubber balloon has an excess of electrons and the animal fur has a shortage of electrons. Having an excess of electrons, the rubber balloon is charged negatively. Similarly, the shortage of electrons on the animal fur leaves it with a positive charge. The two objects have become charged with opposite types of charges as a result of the transfer of electrons from the least electron-loving material to the most electron-loving material.

Two rubber balloons can be suspended from the ceiling and hung at approximately head height. When rubbed upon a teacher's head, the balloons became charged as electrons are transferred from the teacher's fur to the balloons. Since the teacher's fur lost electrons, it became positively charged and the subsequent attraction between the two rubbed objects could be observed. Of course, when the teacher pulls away from the balloons, the balloons experienced a repulsive interaction for each other.

2) Charging by Induction

when a charged body is placed near a neutral body, the charged body attracts opposite charge and repels similar charged present in the neutral body, as a result of this one side of neutral body becomes excess in positive charge while the other side become excess in negative charged this process is called electrostatic induction. 

There are so many method for charging a body by induction method a brief overview is given in following two diagrams

in the next method we use grounding to charge a body as shown in fig.

Conductor and Insulator 

It is convenient to classify substances 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.
When a conductor is connected to the Earth by means of a conducting wire or pipe, it is said to be grounded. The Earth can then be considered an infinite “sink” to which electric charges can easily migrate.

Superconductor is a material that can conduct electricity or transport electrons from one atom to another with no resistance. This means no heat, sound or any other form of energy would be released from the material when it has reached the temperature at which the material becomes superconductive.