9 min readConcept sheetSection A MCQ (1 mark) and match-the-columns parts on units; Section B very short answer (2 marks) on defining the volt or a V = W/q numerical

Electrostatic potential and potential difference: the volt

Potential difference is the work done per unit charge, V = W/q, measured in volts. Positive charge flows from higher to lower potential until the two potentials are equal.

Electrostatic potentialV = W/q: work done to bring a unit positive charge from infinity to the point; near a charge Q, V = kQ/r

Potential differenceV = W/q: work done to move a unit positive charge from one point to the other

The volt1 V = 1 J/C (joule per coulomb)

VoltmeterMeasures potential difference; joined in parallel

Why charges have potential energy

Give a glass rod some positive charge. To add more positive charge, you must push it in against the repulsion of the charge already there. That work is stored as electrostatic potential energy. It is like lifting a stone against gravity: the work done is stored as gravitational potential energy. If a charge q is brought to a distance r from a charge Q, its potential energy is U = kQq/r.

Potential and potential difference

Electrostatic potential at a pointThe work done in bringing a unit positive charge from infinity to that point: V = W/q. Near a charge Q, V = kQ/r.

Unitjoule per coulomb (J C⁻¹), called the volt (V) after Alessandro Volta.

1 voltA point is at 1 V when it takes 1 J of work to bring 1 C of positive charge to it from infinity.

Potential difference (p.d.)The work done in moving a unit positive charge from one point to another: V = W/q.

ScalarPotential and potential difference have size but no direction.

Which way charge flowsPositive charge flows from higher to lower potential; electrons flow the other way. The flow stops when the two potentials are equal.

Potential vs potential difference

Potential at a pointWork per unit charge to bring a positive charge from infinity to one point. It belongs to a single point.

Potential differenceWork per unit charge to move a positive charge between two points. A cell keeps a steady p.d. across a circuit, so charge keeps flowing.

A voltmeter always measures a potential difference. Join it in parallel, across the two points.

Work and potential difference

Problem

(a) How much work is done in moving a charge of 2 C across the terminals of a 9 V battery? (b) 60 J of work moves 5 C of charge between two points. Find the potential difference.

Working

(a) Given: q = 2 C, V = 9 V. Formula: W = qV.
W = 2 C × 9 V = 18 J.
(b) Given: W = 60 J, q = 5 C. Formula: V = W/q.
V = 60 J ÷ 5 C = 12 V.

Answer

(a) 18 J; (b) 12 V

Potential near a charge

Problem

A small sphere carries a charge of 2 × 10⁻⁹ C. Find the potential at a point 10 cm from it, and the potential energy of a 1 μC charge placed there. (k = 9 × 10⁹ N m² C⁻²)

Working

Given: Q = 2 × 10⁻⁹ C, r = 10 cm = 0.10 m.
V = kQ/r = (9 × 10⁹ × 2 × 10⁻⁹) ÷ 0.10 = 18 ÷ 0.10 = 180 V.
Potential energy U = qV = (1 × 10⁻⁶ C) × 180 V = 1.8 × 10⁻⁴ J.

Answer

Potential = 180 V; potential energy = 1.8 × 10⁻⁴ J

In real life

A torch cell gives 1.5 V and a phone battery about 3.7 V: each volt means one joule of energy for every coulomb that passes. A bird can sit safely on one overhead wire, because both its feet are at the same potential and no current flows through it.

Exam angle

1 marks: “Write the SI unit of electric potential.” The volt (V), which is one joule per coulomb.

2 marks: “Define 1 volt of potential difference.” 1 V is the potential difference between two points when 1 J of work moves 1 C of positive charge from one point to the other.

2 marks: “Define potential difference. 150 J of work moves 25 C of charge between two points. Find the potential difference.” Work done per unit charge to move a positive charge between two points. V = W/q = 150 J ÷ 25 C = 6 V.

Remember it

Volts are joules per coulomb: V = W/q. Charge rolls downhill in potential, from high to low, like water.