Class 11 Physics — Chapter 304: Electrostatics

Key concepts: Electrostatics (Class 11 Physics)

Electrostatics from first principles: the three properties of charge, Coulomb's law and how a medium weakens it, the electric field and its lines, the electric dipole and the torque it feels, and Gauss's law with the three standard symmetries it makes trivial. Energy in electrostatics: potential and potential energy, how the field is the negative gradient of potential, equipotential surfaces, conductors and electrostatic shielding, dielectrics and polarisation, capacitance and the parallel plate capacitor, series and parallel combinations, and the energy stored in a charged capacitor.

Properties of electric charge

Charge is additive, is conserved in every process, and is quantised in multiples of the elementary charge e = 1.6 × 10⁻¹⁹ C.

Quantisation of charge

Any observable charge is an integral multiple of e, so a body can never carry a charge like 1.5e. Free quarks, with fractional charge, are never observed in isolation.

Conservation of charge

The total charge of an isolated system is constant. Charging by friction transfers electrons between bodies; it never creates or destroys charge.

Coulomb's law

The force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation, acting along the line joining them.

Effect of a medium

Placing a dielectric of constant K between charges reduces the force by a factor of K, since the medium polarises and partially cancels the field.

Superposition principle

The force on a charge from several others is the vector sum of the individual pairwise forces, each computed as though the others were absent.

Electric field

The force per unit positive test charge at a point, a vector field with units of N C⁻¹ or equivalently V m⁻¹. It exists whether or not a test charge is present.

Electric field lines

Start on positive charge and end on negative, never intersect (the field has one direction at each point), and are denser where the field is stronger.

Electric dipole

A pair of equal and opposite charges separated by a small distance — the model for polar molecules such as water and HCl.

Electric dipole moment

The product of one charge and the separation, a vector pointing from the negative to the positive charge, with unit coulomb-metre.

Field of a dipole

Falls off as the CUBE of distance, faster than a point charge's inverse square. The axial field is twice the equatorial field at the same distance.

Torque on a dipole

A uniform field exerts no net force on a dipole but does exert a torque p × E that tends to align it with the field.

Electric flux

The number of field lines crossing a surface, E·A. It is a scalar and is maximum when the surface is perpendicular to the field.

Gauss's law

The total flux through any closed surface equals the enclosed charge divided by ε₀. Charges outside the surface contribute exactly zero net flux.

Applications of Gauss's law

Yields the field of an infinite wire, an infinite sheet and a charged shell in a line of working — provided the chosen surface matches the symmetry.

Field inside a conductor

Zero everywhere inside a conductor in electrostatic equilibrium, so any excess charge resides entirely on the outer surface.

Electrostatic potential energy

The work done by an external agent in assembling a configuration of charges from infinite separation, brought together without acceleration.

Electric potential

The potential energy per unit charge at a point, measured in volts. It is a SCALAR, which makes it far easier to work with than the field.

Potential of a point charge

Varies as q/r and, unlike the field, carries the sign of the charge — so the potential near a negative charge is genuinely negative.

Relation between E and V

The field is the negative gradient of potential, E = −dV/dr. Field points from high to low potential, in the direction of steepest fall.

Equipotential surfaces

Surfaces of constant potential, always perpendicular to the field lines. No work is done moving a charge anywhere along one.

Potential due to a dipole

Falls off as 1/r² and is ZERO everywhere on the equatorial plane, where the contributions of the two charges cancel exactly.

Potential energy of a system

The sum of the pairwise potential energies of every distinct pair of charges in the configuration.

PE of a dipole in a field

Equal to −p·E, so it is minimum when the dipole aligns with the field (stable) and maximum when anti-parallel (unstable).

Conductors in electrostatics

Field inside is zero, the whole conductor is at one potential, excess charge sits on the surface, and the surface field is perpendicular to it.

Electrostatic shielding

A cavity inside a conductor has zero field regardless of external charges — the principle behind the Faraday cage and why a car is safe in lightning.

Dielectrics and polarisation

An insulator placed in a field develops an induced dipole moment that opposes the applied field, reducing the net field inside by a factor K.

Capacitance

The charge stored per unit potential difference, measured in farads. It is fixed by geometry and the dielectric alone, never by the charge stored.

Parallel plate capacitor

Its capacitance rises with plate area and falls with separation. Inserting a dielectric of constant K multiplies the capacitance by K.

Capacitors in series and parallel

Series capacitors share the same CHARGE and their reciprocals add; parallel capacitors share the same VOLTAGE and simply add. This is opposite to resistors.

Energy stored in a capacitor

Equal to ½CV², the work done in charging it. Half the energy supplied by a battery is always lost as heat during charging.

Energy density of the field

The stored energy can be regarded as residing in the field itself, at ½ε₀E² per unit volume — a picture essential for electromagnetic waves.