COURSE NAME
Physics Chapter-1

Electric Charge and Fields 

Electric Charge

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.

• Electromagnetism is the phenomenon of the interaction of electric currents or fields and magnetic fields.

• When insulating surfaces are rubbed against each other, a static charge is developed which gets discharged after getting in contact with a conductor.

• Only one of the two charges(or polarity) gets developed on rubbing – positive or negative. An object becomes positively charged when it loses the loosely bound electrons to another object while rubbing. The other object gains electrons and becomes negatively charged.

• When like charges are brought near, they repel each other. Unlike charges, they attract each other.

• The charges get neutralized when the two bodies are brought in contact.

• An example of electric charge generation through rubbing of glass rod with silk and plastic rod with silk is mentioned below:

Conductors and Insulators

• Semiconductors offer resistance to the movement of charges which is between conductors and non-conductors.

• The process where excess charge from a body or object goes to the ground, by touching the charge-carrying conducting body to earth is called earthing or grounding.

Charging by Contact

When a charged object is touched by another object, the other object also gets charged with the same polarity due to charge transfer. This is called charge by contact.

Charging by Induction

When a charged object is brought closer to another object (not touched), the original object doesn’t lose any charge and the other object gets charged as well with opposite polarity. The other end of the newly charged object develops polarity same as that of the charged object. This type of charging is called charge by induction.

Properties of electric charge

Electric charge for a body is considered as Point charges if their size is very small in comparison to the distance between them. So the charge is considered to be concentrated at one point. Following are the properties of electric charge in terms of point charges:

1. Additivity of charges:

• Point charges are scalars and can be added algebraically. If q1, q2, q3, … qn, are point charges, the total charge qtot=q1+ q2 + q3+ qn

• Charges have no direction but can be positive or negative.

2. Conservation of charges:

• The total charge in an isolated system is always conserved. When there are many bodies in an isolated system, the charges get transferred from one body to another but the net charge of the system remains the same.

• During rubbing or natural forces, no new charge is created. The charges are either redistributed or a neutron breaks up into proton and electron of equal and opposite charge.

3. Quantization of charges:

   • The charge is always represented in the form of, q = ne. Here n is an integer and e is the charge (- for electron and + for proton). Magnitude of e = 1.602192 X 10-19 This is called quantization of charge.

   • SI unit of charge is Coulomb (C).

   • Quantization is usually ignored at macroscopic levels (μC) because, at that point, charges are taken to be continuous.

Coulomb’s Law

Coulomb’s law states that Force exerted between two point charges:

• Is inversely proportional to the square of the distance between these charges and

• Is directly proportional to the product of the magnitude of the two charges

• Acts along the line joining the two-point charges.

Here ε0 = 8.854 x 10-12 C2 N-1 m-2 is called the permittivity of free space.

Forces between multiple charges –Superposition principle

As per the principle of superposition, the force on any charge due to several other charges is the vector sum of all the forces on that charge due to other charges, taken one at a time.

Electric Field

The electric field is a force produced by a charge near its surroundings. This force is exerted on other charges when brought in the vicinity of this field.

• SI unit of the electric field is N/C (Force/Charge).

• An electric field due to a charge at a point is the force that a unit positive charge would experience if placed at that point.

• The charge-generating electric field is called source charge and the charge which experiences this field is called test charge. Practically, to keep the source charge undisturbed due to the electric field of the test charge, the test charge is kept infinitely small.

• Since F(Force) is proportional to q (Charge), the electric field is independent of q but depends on r (space coordinates).

• The electric field is symmetric in spherical coordinates.

• The concept of Electric field is used to account for the time delay for a charged body to experience force from the field of a source charge.

Electric field due to system of charges

According to the superposition principle, the total electric field at a point in space is equal to the vector sum of individual fields present.

Electric Field Lines

Electric field lines are a pictorial way of representing an electric field around a configuration of charges.

• An electric field line is a curve drawn in such a way that the tangent to it at each point is in the direction of the net field at that point.

• The electric field is inversely proportional to the square of the distance; hence electric field near the charge is high and keeps on decreasing as we go farther from the charge. The electric field lines, however, remain constant but are very far apart (at higher distances) as compared to lesser distances.

Electric Flux

Electric flux is the measure of the flow of the electric field through a given area. Electric flux is proportional to the number of electric field lines going through a normally perpendicular surface.

• The orientation of the area element decides the amount of electric flux. Thus, the area element is a vector.

• The vector associated with every area element of a closed surface is taken to be in the direction of the outward normal.

• Area element vector ΔS = ΔSn̂, ΔS is the magnitude of the area element and n̂ is the unit vector in the direction of outward normal.

• Electric flux, Δφ = EΔS = E ΔScosθ, θ is the angle between E and ΔS.

• The unit of electric flux is NC-1m2.

• Total flux through a surface, φ ≈ Σ EΔS