ELECTRIC FORCE AND ELECTRIC CHARGE

ELECTRIC FORCE AND ELECTRIC CHARGE
1.Introduction
Ordinary matter consists of atoms. Each atom consists of a nucleus containing protons and neutrons, surrounded by a number of electrons. The masses of the electrons, protons and neutrons are listed in Table 1. Most of the mass of the atom is due to the mass of the nucleus.
particle mass (m in kg)
electron 9.11 x 10-31
proton 1.673 x 10-27
neutron 1.675 x 10-27

Table 1. Masses of the building blocks of atoms.

The diameter of the nucleus is between 10-15 and 10-14 m. The electrons are contained in a roughly spherical region with a diameter of about 2 x 10-10 m. Measurements of the velocity of the orbital electrons in an atom have shown that the attractive force between the electrons and the nucleus is significantly stronger than the gravitational force between these two objects. The attractive force between the electrons and the nucleus is called the electric force.

Experiments have shown that the electric force between two objects is proportional to the inverse square of the distance between the two objects. The electric force between two electrons is the same as the electric force between two protons when they are placed at the same distance. This implies that the electric force does not depend on the mass of the particle. Instead, it depends on a new quantity: the electric charge. The unit of electric charge q is the Coulomb (C). The electric charge can be negative, zero, or positive. The electric charge on a glass rod rubbed with silk is positive. The electric charge of electrons, protons and neutrons are listed in Table 2. Detailed measurements have shown that the magnitude of the charge of the proton is exactly equal to the magnitude of the charge of the electron. Since atoms are neutral, the number of electrons must be equal to the number of protons.

2. Charge:
• there are two kinds of charge, positive and negative
• like charges repel, unlike charges attract
• positive charge comes from having more protons than electrons; negative charge comes from having more electrons than protons
• charge is quantized, meaning that charge comes in integer multiples of the elementary charge e
• charge is conserved
Probably everyone is familiar with the first three concepts, but what does it mean for charge to be quantized? Charge comes in multiples of an indivisible unit of charge, represented by the letter e. In other words, charge comes in multiples of the charge on the electron or the proton. These things have the same size charge, but the sign is different. A proton has a charge of +e, while an electron has a charge of -e.

Electrons and protons are not the only things that carry charge. Other particles (positrons, for example) also carry charge in multiples of the electronic charge. Putting "charge is quantized" in terms of an equation, we say:
q = n e
q is the symbol used to represent charge, while n is a positive or negative integer, and e is the electronic charge, 1.60 x 10-19 Coulombs.
The Law of Conservation of Charge
The Law of conservation of charge states that the net charge of an isolated system remains constant.

If a system starts out with an equal number of positive and negative charges, there’s nothing we can do to create an excess of one kind of charge in that system unless we bring in charge from outside the system (or remove some charge from the system). Likewise, if something starts out with a certain net charge, say +100 e, it will always have +100 e unless it is allowed to interact with something external to it.
Table of elementary particle masses and charges:
Table 2:


3. Electrostatic charging
Forces between two electrically-charged objects can be extremely large. Most things are electrically neutral; they have equal amounts of positive and negative charge. If this wasn’t the case, the world we live in would be a much stranger place. We also have a lot of control over how things get charged. This is because we can choose the appropriate material to use in a given situation.

Metals are good conductors of electric charge, while plastics, wood, and rubber are not. They’re called insulators. Charge does not flow nearly as easily through insulators as it does through conductors, which is why wires you plug into a wall socket are covered with a protective rubber coating. Charge flows along the wire, but not through the coating to you.
Materials are divided into three categories, depending on how easily they will allow charge (i.e., electrons) to flow along them. These are:
• conductors - metals, for example
• semi-conductors - silicon is a good example
• insulators - rubber, wood, plastic for example
Most materials are either conductors or insulators. The difference between them is that in conductors, the outermost electrons in the atoms are so loosely bound to their atoms that they’re free to travel around. In insulators, on the other hand, the electrons are much more tightly bound to the atoms, and are not free to flow. Semi-conductors are a very useful intermediate class, not as conductive as metals but considerably more conductive than insulators. By adding certain impurities to semi-conductors in the appropriate concentrations the conductivity can be well-controlled.

There are three ways that objects can be given a net charge. These are:

1. Charging by friction - this is useful for charging insulators. If you rub one material with another (say, a plastic ruler with a piece of silk), electrons have a tendency to be transferred from one material to the other. For example, rubbing glass with silk generally leaves the glass with a positive charge.

2. Charging by conduction - useful for charging metals and other conductors. If a charged object touches a conductor, some charge will be transferred between the object and the conductor, charging the conductor with the same sign as the charge on the object.

3. Charging by induction - also useful for charging metals and other conductors. Again, a charged object is used, but this time it is only brought close to the conductor, and does not touch it. If the conductor is connected to ground (ground is basically anything neutral that can give up electrons to, or take electrons from, an object), electrons will either flow on to it or away from it. When the ground connection is removed, the conductor will have a charge opposite in sign to that of the charged object. A practical application involving the transfer of charge is in how laser printers and photocopiers work .
Why is static electricity more apparent in winter?
You notice static electricity much more in winter (with clothes in a dryer, or taking a sweater off, or getting a shock when you touch something after walking on carpet) than in summer because the air is much drier in winter than summer. Dry air is a relatively good electrical insulator, so if something is charged the charge tends to stay. In more humid conditions, such as you find on a typical summer day, water molecules, which are polarized, can quickly remove charge from a charged object.

4. Coulomb’s Law of Electric force
The precise magnitude of the electric force that a charged particle exerts on another is given by Coulomb's law:
" The magnitude of the electric force that a particle exerts on another particle is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The direction of the force is along the line joining the particles. "

The electric force Fc can be written as
… … … (1)
where
q1 and q2 are the charges of particle 1 and particle 2, respectively
r is the distance between particle 1 and particle 2 (see Figure 1)
[epsilon]0 is the permittivity constant: [epsilon]0 = 8.85 x 10-12 C2/(N . m2)
This formula applies to elementary particles and small charged objects as long as their sizes are much less than the distance between them.

Figure 1. Electric force between two charged objects.
An important difference between the electric force and the gravitational force ( where m1, m2 are the masses of two bodies and r is the distance between them. G is a constant: G = ) is that the gravitational force is always attractive, while the electric force can be repulsive (Fc > 0), zero, or attractive (Fc < 0), depending on the charges of the particles. Table 3 lists the gravitational and the Coulomb force between electrons, protons and neutrons when they are separated by 1 x 10-10 m.
Our discussion of the electric force will initially concentrate on those cases in which the charges are at rest or are moving very slowly. The electric force exerted under these circumstances is called the electrostatic force. If the charges are moving with a uniform velocity, they will experience both the electrostatic force and a magnetic force. The combined electrostatic and magnetic force is called the electromagnetic force.

particle-particle Fg (N) Fc (N)
electron - electron -5.5 x 10-51 2.3 x 10-8
electron - proton -1.0 x 10-47 - 2.3 x 10-8
electron - neutron -1.0 x 10-47 0
proton - proton - 1.9 x 10-44 2.3 x 10-8
proton - neutron - 1.9 x 10-44 0
neutron - neutron - 1.9 x 10-44 0
Table 3. The gravitational (Fg) and Coulomb (Fc) between the building blocks of atoms.

Electric current: The rate of flow of electric charge is called electric current and is measured in amperes.
Amperes = coulomb/second
where, I = electric current, Q = electric charge, and t = time
Although it is electrons which are the mobile charge carriers which are responsible for electric current in conductors such as wires, it has long been the convention to take the direction of electric current as if it were the positive charges which are moving.

In a direct current (DC) electrical circuit, the voltage (V in volts) is an expression of the available energy per unit charge, which drives the electric current (I in amperes) around a closed circuit. Increasing the resistance (R in ohms) will proportionately decrease the current, which may be driven through the circuit by the voltage.

Resistance: Resistance of any material is the property of that material for which it resists the flow of current through it. Unit of resistance is ohm.
Ohm's Law:
For the conductors of electricity, the electric current, which will flow through them, is directly proportional to the voltage applied to them provided the temperature remains constant. The ratio of voltage to current is called the resistance, and if the ratio is constant over a wide range of voltages, the material is said to be an "ohmic" material. If the material can be characterized by such a resistance, then the current can be predicted from the relationship: