6.2FieldsStretch

Electric Potential

Electric potential works exactly like gravitational potential — energy per unit charge instead of energy per unit mass — but with one key twist: because charge can be positive or negative, electric potential can be positive, negative, or zero, unlike its gravitational counterpart.

40 min Video by Mr Turnbull’s Physics Module 6.2 Electric fields

Electric Potential Energy — OCR A-Level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Define electric potential and use $V = \frac{Q}{4 π ε _{0} r}$
Calculate potential energy of a charge in an electric field
Calculate work done moving a charge between two points
Describe equipotential surfaces

Electric potential

Electric potential, $V$ , is the work done per unit positive charge bringing a test charge from infinity to a point. It takes the same sign as the source charge — positive around a positive charge, negative around a negative charge.

V = \frac{Q}{4 π ε _{0} r}

Electric potential due to a point charge.

1Use

V = \frac{Q}{4 π ε _{0} r}

V = \frac{- 5.0 \times 1 0 ^{- 9}}{4 π \times 8.85 \times 1 0 ^{- 12} \times 0.25}

Answer

V \approx - 180

Potential energy and work done

The potential energy of a charge $q$ at potential $V$ is $E_{p} = q V$ . Moving a charge through a potential difference requires (or releases) energy $W = q Δ V$ .

E_{p} = q V W = q Δ V

Electric potential energy and work done.

1Use

W = q (V_{2} - V_{1})

W = 3.0 \times 1 0^{- 6} \times (120 - 200) = 3.0 \times 1 0^{- 6} \times (- 80)

Answer

W = - 2.4 \times 1 0^{- 4}

J — energy is released, since the positive charge moves from high to low potential.

Equipotentials

Equipotential surfaces join points of equal potential, are always perpendicular to field lines, and require zero work to move a charge along them.

Equation recap

V = \frac{Q}{4 π ε _{0} r}

Electric potential.

E_{p} = q V, W = q Δ V

Potential energy and work done.

Common mistakes to avoid

Assuming electric potential, like gravitational potential, is always negative.

Electric potential takes the sign of its source charge — positive, negative, or zero.

Forgetting the sign of the moving charge in W=qΔV.

A negative charge moving through a positive ΔV releases energy — the opposite of a positive charge in the same field.

Key takeaways

Electric potential V = Q/(4πε₀r), same sign as the source charge.
Potential energy Ep=qV; work done W=qΔV.
Equipotentials are perpendicular to field lines; zero work along them.

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Electric Potential

40 min Video by Mr Turnbull’s Physics Module 6.2 Electric fields