Electric Charge

• The property of matter due to which matter shows electric and magnetic effects is called Charge.
• Charge may be fundamental property or may be acquired.
• Electrons and protons have fundamental charges, other bodies acquire charge.
• Charge is scalar quantity.
• SI unit of charge is coulomb (C).
• Dimension of charge [AT].

Types of charge: 

1. Positive charge
2. Negative charge

Properties of charge:

1. Like charges repel and unlike charges attract (fundamental law of electrostatics)
2. Law of conservation of charge – in an isolated system total charge remains conserved. eg – Pair production and annihilation.
3. Additive Property – charge being scalar quantity, can be added algebraically, considering the sign of the charges. For continuous charge distribution integration is used. 
4. Charge is invariant : This means that charge is independent of frame of reference, i.e., charge on a body does not change whatever be its speed.
5. Quantization of charge – Total charge on a body is an integral multiple of electronic charge.

         q = ne, n is integer then only charge is possible. 

• we can ignore quantisation of charge for macroscopic objects

Comparison between charge and mass.

• Charge can’t exist without mass but mass may exist without charge.
• Specific Charge (q/m):It is defined as the ratio of charge and mass.

Methods of charging:

• Charging by friction: when two objects are rubbed against each other energy is provided to remove electrons from one object to another this method of charging is known as charging by friction.
• Electrons are transferred from a body of lower work function to a body of higher work function.
• Cause of charging by friction: Charging by friction is due to actual transfer of electrons from one body to another.
• The body which loses electrons acquires positive charge and the body which gains electrons acquires negative charge.
• With transfer of charge there occurs transfers of mass as well.

Charging by conduction 

• When a charged body is brought in contact with an uncharged body some of the charge is transferred from the charged body to the uncharged body, this is called charging by conduction.
• Both the bodies acquire the same kind of charge.
• If both the bodies brought in contact were charged then their final nature depends on the sum of two charges.
• For identical bodies charge gets equally distributed between them.
• For sphere of different radii :q‘/r = constant, q‘ is the final charge and r is radius.

Gold-leaf electroscope

• It is an instrument which is used to detect the presence of charge.
• It consists of a vertical metal rod placed in a box, with two thin gold leaves attached to its bottom end.
• When a charged object touches the metal knob at the top of the rod, charge flows on to the leaves and they diverge. There will be no divergence if the body is uncharged. The degree of divergence is an indicator of the amount of charge.

Charging by Induction

• The phenomenon of temporary electrification of conductors in which there is separation of charge in such a way that opposite charge appears at closer end and similar charge appears at farther end in presence of nearby charged body.
• The centres of the two types of charges are slightly separated. We know that opposite charges attract while similar charges repel. However, the magnitude of force depends on the distance between the charges and in this case the force of attraction overweighs the force of repulsion. As a result the particles like bits of paper or pith balls, being light, are pulled towards the rods.
• Amount of induced charge: q’=-q(1-1/k), for air k  =1 and for metal k = infinity

1. How can you charge a metal sphere positively without touching it?
2. Why can we ignore quantisation of charge for macroscopic objects?Ans – The magnitude of charge on an electron is too small to be compared with the magnitude of charge involved in the case of electrically charged large objects.
3. Why is repulsion considered a sure test of presence of charge?

        Ans – Attraction is possible between a neutral body and a charged body but repulsion is possible only between two likely charged bodies, hence repulsion is considered a sure test of presence of charge.

Continuous charge distribution

1. Linear charge density –  it is defined as the charge per unit length if charge is distributed along one dimensional curve or line. SI unit coulomb per metre.
2. Surface charge density –  it is defined as charge per unit area when charge distribution spreads over a two-dimensional surface. SI unit  coulomb per metre square
3. Volume charge density – it is defined as charge contained per unit volume when charge distribution is spread over three dimensional volume. SI unit coulomb per metre cube .