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Potentials and Equipotentials

Reading field strength from equipotential spacing and calculating work done.

  • Define and explain Potentials and Equipotentials in your own words
  • Use key terms such as equipotential accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Potentials and Equipotentials: reading field strength from equipotential spacing and calculating work done.

Definition: Potentials and Equipotentials

Reading field strength from equipotential spacing and calculating work done.

Key ideas

Fields are mapped with lines

Field lines show direction — the way a test mass or positive charge would be pushed — and spacing shows strength: closer lines mean a stronger field. Gravitational and electric field lines radiate from masses and charges; magnetic field lines form closed loops, emerging from north poles and entering south poles.

Inverse-square laws govern point sources

Around a point mass, g = GM/r²; around a point charge, E = Q/(4πε₀r²). Doubling the distance quarters the field strength — the same mathematics in both cases, hinting at a deep unity. Inside a uniform field, like between charged plates, E = V/d is constant everywhere.

Key term — equipotential: A line or surface where the potential is constant — no work is done moving along it.

Worked example: Potentials and Equipotentials

Why is no work done moving a charge along an equipotential?

Potential is constant along an equipotential, so ΔV = 0 and W = QΔV = 0.

Answer: Potential is constant along an equipotential, so ΔV = 0 and W = QΔV = 0.

Common mistakes
  • Confusing electric potential with field strength Potential (V) is energy per unit charge; field strength (V/m) is its gradient — E = −ΔV/Δx.
  • Drawing field lines crossing Field lines never cross — a crossing would mean two field directions at one point, which is impossible.

Practice

A 0.3 m wire carrying 2 A sits perpendicular to a 0.5 T field. Find the force on it.
F = BIl.

0.5 × 2 × 0.3 = 0.3 N.

Describe the electric field pattern around an isolated positive point charge.
Which way would a positive test charge be pushed?

Radial lines pointing straight outwards from the charge, getting further apart with distance as the field weakens.

Use Fleming's left-hand rule: magnetic field into the page, current to the right. Which way is the force?
First finger field, second finger current.

Upwards — with the first finger pointing into the page and the second finger to the right, the thumb points up.

Earth's mass is 6.0 × 10²⁴ kg. Calculate g at 6.4 × 10⁶ m from its centre (G = 6.67 × 10⁻¹¹ N m²/kg²).
g = GM/r².

(6.67 × 10⁻¹¹ × 6.0 × 10²⁴) ÷ (6.4 × 10⁶)² = 4.0 × 10¹⁴ ÷ 4.096 × 10¹³ ≈ 9.8 N/kg.

Quick check

Potentials and Equipotentials — quick check

Which of these best defines "equipotential"?

A line or surface where the potential is constant — no work is done moving along it.

A satellite orbits at twice Earth's radius from the centre. How does g there compare to the surface value?

g ∝ 1/r², so doubling r quarters g — about 9.8 ÷ 4 ≈ 2.45 N/kg.
Key takeaways
  • Potentials and Equipotentials: reading field strength from equipotential spacing and calculating work done.
  • Fields are mapped with lines: Field lines show direction — the way a test mass or positive charge would be pushed — and spacing shows strength: closer lines mean a stronger field.
  • field strength: Force per unit mass (N/kg) or per unit charge (N/C) at a point in the field.
  • Watch out for: confusing electric potential with field strength
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