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A Level Electric Fields Hub

A Level Physics electric fields hub: Coulomb's Law, electric potential, uniform fields, and capacitance.

  • GCE A-Level H2 Physics 2027
Learning goals
  • Apply Coulomb's law to the force between point charges.
  • Define electric field strength and calculate resultant fields due to point charges.
  • Define electric potential and calculate potential due to point charges.
  • Relate electric potential, potential energy and work for systems of point charges.
  • Use the negative potential gradient and relate equipotentials to field lines.
  • Calculate field strength and force in uniform electric fields.
  • Analyse charged-particle motion in uniform electric fields.
  • Apply capacitance and capacitor-energy relationships.

Electric Fields connects force, energy and motion through two linked descriptions: the vector field vector E and the scalar potential V. Follow the route below in order so that point-charge, uniform-field and capacitor equations are used with the correct model and sign convention.

Start here

Understand first: revise field lines in O-Level Static Electricity, vector addition in Vector Addition and Components, and the field–potential analogy in Gravitation.

Common mark-loss errors: confusing E ∝ 1/r² with V ∝ 1/r, treating potential as a vector, reversing electron force direction, and writing W_field = qΔ V instead of W_field = -qΔ V.

Lessons

Work through these lessons in order.

  1. Coulomb force between point charges
  2. Electric field strength due to a point charge
  3. Potential, potential energy and negative gradient
  4. Uniform fields, force and charged-particle motion
  5. Capacitance and stored electric potential energy
  6. Coulomb's Law

    Use Coulomb’s law to calculate the electric force between point charges, including direction (attraction/repulsion) and inverse-square scaling (A Level Physics).

  7. Electric Field Strength of a Point Charge

    Define electric field strength, calculate the field due to point charges, determine direction, and apply vector superposition.

  8. Electric Potential

    Define electric potential as work done per unit charge from infinity, use V = (1/4πϵ0)Q/r, and apply E = −dV/dr (A Level Physics).

  9. Electric Potential Energy

    Relate electric potential energy to potential using U = qV, use U = kQq/r for point charges, and apply work–energy links for moving charges (A Level Physics).

  10. Equipotential Lines

    Explain equipotential lines/surfaces, relate them to electric field lines, and use E as the negative potential gradient (A Level Physics).

  11. Uniform Electric Fields (Parallel Plates)

    Use E = V/d and F = qE to analyse uniform electric fields and the motion of charged particles between parallel plates (A Level Physics).

  12. Acceleration Due to an Electric Field

    Use F = qE and a = qE/m for charged particles in uniform fields, including kinematics and energy methods (A Level Physics).

  13. Capacitance

    Use C = Q/V and the V–Q graph area to solve capacitance and energy stored in a capacitor questions (A Level Physics).

  14. Questions for Electric Field (JC) Set 1

    A Level Physics electric fields practice questions (JC Set 1), with worked answers.

Revision

Quick Reference
QuantityPoint-charge formulaUniform-field formula
Force (F)F = (| Qq|)/(4πε₀ r²)vector F = q vector E
Field strength (E)E = (| Q|)/(4πε₀ r²)| E| = (|Δ V|)/d
Potential (V)V = Q/(4πε₀ r)Δ V = -EₓΔ x
Potential energy (U)U = Qq/(4πε₀ r)U = qV

Capacitor: C = Q/V, Energy U = (1/2)CV²

Exam Templates (fast marks)

Point charge questions

  1. Sketch the situation and define r (centre-to-centre distance).
  2. Use either F = Qq/(4πε₀ r²) or E = Q/(4πε₀ r²), then link with F = qE.
  3. Add direction: field points away from + charge and toward − charge; force direction depends on sign of test charge.

Uniform field between plates

  1. Use E = V/d (magnitude) and decide sign with a chosen axis.
  2. Force: F = qE; acceleration: a = qE/m.
  3. Treat motion like a projectile: constant horizontal velocity, constant vertical acceleration.

Energy and potential

  1. Potential-energy change: Δ U = qΔ V.
  2. Work done by the field: W_field = -Δ U = -qΔ V; slow external work is the opposite.
  3. For capacitors: U = (1/2)CV² = (1/2)QV = Q²/2C (choose the form with known quantities).
Graph Skills (Exam + Practical)

Inverse-square vs inverse (field vs potential)

For a point charge, field strength falls with 1/r², while potential falls with 1/r (more slowly). This is why potential “extends” further than field.

How E and |V| change with distance (point charge)

Scaled plot showing electric field strength falling with 1/r^2 and potential magnitude falling with 1/r.

Scroll across the graph to read all labels.

Scaled plot showing electric field strength falling with 1/r^2 and potential magnitude falling with 1/r.Scaled plot showing electric field strength falling with 1/r^2 and potential magnitude falling with 1/r.
The sign of V depends on the sign of the source charge; the plot shows magnitudes so you can compare how fast each falls off.
Open full-size graph
View figure data
Values for How E and |V| change with distance (point charge)
Distance from charge (r / R)Field strength, E ∝ 1/r²Potential magnitude, |V| ∝ 1/r
111
20.250.5
30.1110.333
40.06250.25
50.040.2
60.02780.1667

Uniform field: potential changes linearly with distance

Between parallel plates (uniform field), potential varies linearly with distance, and the field strength is the negative gradient: E = -dV/dx (magnitude: E = ((Δ V)/d))

Potential vs distance in a uniform field (example)

A straight-line potential-distance graph between parallel plates; the gradient gives the electric field strength.

Scroll across the graph to read all labels.

A straight-line potential-distance graph between parallel plates; the gradient gives the electric field strength.A straight-line potential-distance graph between parallel plates; the gradient gives the electric field strength.
Here ΔV = 10 V across d = 0.05 m, so |E| = ΔV/d = 200 V m⁻¹. Use the sign based on your chosen direction.
Open full-size graph
View figure data
Values for Potential vs distance in a uniform field (example)
Distance from plate, x (m)V(x) (linear)
010
0.018
0.026
0.034
0.042
0.050

Capacitor energy: quadratic in V

For a fixed capacitance, energy stored is U = (1/2)CV², so a plot of U against V is a curve (not a straight line).

Energy stored vs potential difference (fixed C)

A curve showing that capacitor energy increases with the square of potential difference.

Scroll across the graph to read all labels.

A curve showing that capacitor energy increases with the square of potential difference.A curve showing that capacitor energy increases with the square of potential difference.
Doubling V quadruples U. This is a common sanity check when comparing energy storage at different voltages.
Open full-size graph
View figure data
Values for Energy stored vs potential difference (fixed C)
Potential difference, V (V)U = ½CV² (C = 100 μF)
00
50.00125
100.005
150.01125
200.02
What You Must Memorise
  • Coulomb’s Law: The force between two point charges is proportional to the product of their charges and inversely proportional to the square of their separation.
  • Electric Field Strength (E): Force per unit positive charge acting on a stationary point charge.
  • Electric Potential (V): Work done per unit positive charge in bringing a small test charge from infinity to that point.
  • Capacitance (C): The ratio of charge stored on one plate to the potential difference between the plates.
Top Exam Traps
  1. Analogy with Gravity: Electric force can be repulsive (unlike gravity). Potential can be positive (near +ve charge) or negative (near -ve charge).
  2. Field vs Potential: E = -dV/dr. Field strength is the (negative) gradient of the potential-distance graph.
  3. Work and energy: Δ U = qΔ V, but work done by the field is W_field = -qΔ V.
  4. Uniform vs Point Field: Don’t use kQ/r² for parallel plates. Use E = V/d.
  5. Motion: In a uniform field (like a CRT), an electron follows a parabolic path (like a projectile). In a magnetic field, it follows a circular path.

Practice

Practice (Quiz + Structured Questions)

Test your understanding of Electric Fields:

A Level Electric Fields QuizElectric Fields Structured SetA Level Quiz Hub

The archived JC Set 1 remains available as extra practice after the current quiz and structured set.

Next hub: Currents & Circuits

Back To A Level Physics

Continue with the next resource in this course.

Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027