Electrostatics

Electrostatics deals with charges at rest and the forces, fields, potentials, and energy associated with them. The PMDC MDCAT 2026 syllabus is dense in this chapter — from Coulomb's law and field calculations for points/sheets, to capacitors and RC charging/discharging. Expect 2-3 MCQs.

PMC Table of Specifications. Seven listed subtopics: Charging/Discharging Capacitor, Coulomb's Law, Electric Field, Electric Field of Infinite Sheet, Electric Field Intensity (Point Charge), Electric Field Lines, and Electric Potential Energy & Potential.

Coulomb's Law

Two point charges q₁ and q₂ separated by distance r exert on each other a force directed along the line joining them:

F = k q₁q₂ / r²

where k = 1 / (4πε₀) ≈ 9 × 10⁹ N m² C⁻² in vacuum, and ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻².

Like charges repel; unlike charges attract.
The force obeys Newton's third law (equal and opposite).
In a medium of relative permittivity ε_r, divide the vacuum force by ε_r.
The principle of superposition: net force = vector sum of individual Coulomb forces.

Electric Field

An electric field at a point is the force per unit positive test charge placed there:

E = F / q

SI unit: N C⁻¹ = V m⁻¹. E is a vector quantity in the direction of force on a positive test charge.

Electric Field Intensity (Point Charge)

The field at distance r from a point charge Q in vacuum is

E = kQ / r²

Direction: radially outward for +Q, inward for −Q.

Standard electric-field formulas you should remember
Source	Formula for E	Direction / notes
Point charge Q (vacuum)	E = kQ/r² = Q/(4πε₀r²)	Radial, ∝ 1/r²
Long charged rod (linear density λ)	E = λ/(2πε₀r)	Radial, ∝ 1/r
Infinite charged sheet (σ)	E = σ/(2ε₀)	Perpendicular to sheet, independent of distance
Parallel-plate capacitor (between)	E = σ/ε₀ = V/d	Uniform between plates; zero outside
Inside a conductor (electrostatic)	E = 0	Charge resides on outer surface (Faraday cage)
At centre of a uniformly charged sphere	E = 0	Symmetry → net field cancels
Outside uniformly charged sphere	E = kQ/r²	Behaves like point charge at centre

Field inside a conductor

Under electrostatic equilibrium, the electric field inside a conductor is zero. Any excess charge resides on the outer surface; the conductor itself is at one constant potential (an equipotential volume). This is the principle behind electrostatic shielding.

Electric Field (Infinite Sheet)

A uniformly charged infinite plane of surface charge density σ (C m⁻²) produces a uniform field perpendicular to the sheet on either side:

E = σ / (2ε₀)

The field is independent of distance from the sheet (within the infinite-sheet idealisation).

Two parallel sheets — the parallel-plate capacitor

Two infinite sheets carrying opposite charge densities ±σ produce a uniform field between the plates and zero field outside:

E_between = σ / ε₀

This is twice the single-sheet result — the contributions from the two plates add up between, cancel outside.

Electric Field Lines

Field lines (Faraday's lines of force) provide a visual map of an electric field. Properties to remember:

They begin on positive charges and end on negative charges (or run to infinity).
The tangent at any point gives the direction of E there.
Density of lines (lines per unit perpendicular area) is proportional to the magnitude of E.
Two field lines never cross — the field has a unique direction at every point.
Field lines are perpendicular to a conductor's surface in equilibrium.

Common trap. Electric field lines are not paths of moving charges — they are an instantaneous direction map. A charge starts moving along the line at that instant, but it accelerates and may follow a curved trajectory.

Electric Potential Energy and Potential

The work done by an external agent in bringing a positive test charge q from infinity to a point against the field equals the electric potential energy U at that point.

Electric potential

V = U / q = W / q

Electric potential is potential energy per unit charge. SI unit: volt (V) = J C⁻¹. It is a scalar — no direction, only sign.

Potential due to a point charge

V = kQ / r

(Reference: V = 0 at infinity.) Note V ∝ 1/r, while E ∝ 1/r².

Potential energy of a charge pair

U = k q₁q₂ / r = q₂ V₁

Positive U → like charges (repulsive system). Negative U → unlike charges (bound system).

Relation to field

For a uniform field, V = E d (where d is distance along the field). In general, E = −dV/dx — the field points "downhill" in potential.

Charging and Discharging Capacitor

A capacitor stores charge. For any capacitor: C = Q / V (units: farad, F). For a parallel-plate capacitor in vacuum:

C = ε₀ A / d

Inserting a dielectric of permittivity ε_r multiplies C by ε_r.

Combinations

Series: 1/C_s = 1/C₁ + 1/C₂ + ... ; same charge on each, voltages add.
Parallel: C_p = C₁ + C₂ + ... ; same voltage across each, charges add.
Energy stored: U = ½ CV² = ½ QV = Q²/(2C).

Charging through a resistor (RC circuit)

When a capacitor is charged through a resistor R from a battery of EMF V₀:

V(t) = V₀ (1 − e^−t/τ)

The charge on the capacitor builds up exponentially. The time constant

τ = RC

is the time taken for the capacitor to reach 63% of its final voltage. After 5τ it is essentially fully charged.

Discharging

When a charged capacitor discharges through a resistor:

V(t) = V₀ e^−t/τ

Voltage drops to 37% of its initial value after one time constant.

Time-constant memory aid. "63 up, 37 down" — after one τ, a charging capacitor reaches 63% and a discharging one falls to 37%. After ~5τ the transient is over and the circuit is in steady state.

Worked MCQs

Five MCQs that capture the high-yield testing patterns for this chapter. Read the explanation even when you get the answer right — it's where the deeper concept lives.

Q1. The Coulomb force between two point charges, when the distance between them is doubled, becomes:

Double the original
Half the original
One-third the original
One-quarter the original

F ∝ 1/r². Doubling r quarters the force. The same inverse-square dependence governs gravitation and the electric field of a point charge.

Q2. The electric field inside a conductor in electrostatic equilibrium is:

Zero
Equal to the surface field
Maximum at the centre
Equal to σ/ε₀

If E were non-zero inside a conductor, free electrons would accelerate — not "equilibrium." Excess charge sits on the outer surface, leaving zero field inside. This is why a Faraday cage shields the interior from external fields.

Q3. A 10 µF capacitor is charged through a 200 kΩ resistor. The time constant of the circuit is:

0.2 s
2 s
20 s
200 s

τ = RC = (2 × 10⁵) × (10⁻⁵) = 2 s. After 2 s the capacitor reaches 63% of the supply voltage; after ~10 s (5τ) it is essentially fully charged.

Q4. The electric field due to an infinite plane sheet of charge with surface density σ is:

σ/ε₀
σ/(2ε₀)
σ/(4πε₀)
2σ/ε₀

Single infinite sheet: E = σ/(2ε₀), independent of distance. Between two parallel oppositely charged sheets the fields add and E = σ/ε₀ (and zero outside) — that's the parallel-plate capacitor.

Q5. The energy stored in a capacitor of capacitance C charged to potential V is:

CV
CV²
½ CV²
2 CV²

Energy U = ½ CV² = ½ QV = Q²/(2C). The factor of ½ arises because the voltage rises from 0 to V as charge accumulates — the work integral gives half of QV.

Quick Recap

Coulomb: F = kq₁q₂/r²; k = 9 × 10⁹ N m² C⁻².
Field of a point charge: E = kQ/r²; potential: V = kQ/r.
Inside a conductor in equilibrium: E = 0.
Infinite sheet: E = σ/(2ε₀); parallel-plate capacitor inside: E = σ/ε₀.
Field lines: + to −, never cross, density = magnitude.
Potential energy: U = kq₁q₂/r; V = U/q.
Capacitor: C = Q/V; parallel plate C = ε₀A/d; energy U = ½CV².
Combinations: series 1/C_s = Σ1/C; parallel C_p = ΣC.
RC circuit: τ = RC. Charging V = V₀(1 − e^−t/τ); discharging V = V₀e^−t/τ.

Test yourself. Take a timed Electrostatics quiz or browse all Physics MCQs to lock these concepts in.