Electric Potential | CAIE 9702 Paper 4 Notes

Chapters

Paper 4

Physics9702

Electric Potential

Electric field strength describes force. Electric potential describes energy per unit charge.

For an isolated point charge, the reference value is zero at infinity.

The two-mark definition

Definition

2 marks

What is meant by electric potential at a point?

Model answer: The work done per unit positive charge in bringing a small test charge from infinity to the point.

“Work done per unit charge” and “positive charge from infinity” are the two marking points (9702/41/O/N/25 Q5(a)) (9702/42/M/J/24 Q5(a)).

V=\dfrac{Q}{4\pi\varepsilon_0r}

Symbols

$V$ = electric potential (V)
$Q$ = charge producing the potential (C)
$r$ = distance from the charge or sphere centre (m)

Potential follows an inverse-distance relation, not an inverse-square relation.
A positive source produces positive potential. A negative source produces negative potential.
Potential is a scalar. Add the potential from each charge using its sign; do not resolve directions.

Common mistake

Electric field is a vector, but electric potential is a scalar. Use arrows for field and signed numbers for potential.

Add potential from more than one charge

Swipe left or right to see the whole diagram →

Potential along a proton–electron line (the 2025 exam curve, sampled from V ∝ 1/x − 1/(120 − x)): +130 V at 10 pm, +32 V at 30 pm, zero exactly at the 60 pm midpoint — signed scalars adding, no vectors needed.

Worked example

Potential between a proton and an electron

A proton and an electron are 120 pm apart. Find the total potential 30 pm from the proton.

The point is 90 pm from the electron. Write both signed contributions.
$V=V_{\mathrm p}+V_{\mathrm e}$
$V_{\mathrm p}=+48\ \mathrm{V}$
$V_{\mathrm e}=-16\ \mathrm{V}$
Evaluate the sum.
$V=+32\ \mathrm{V}$

Answer

V=+32\ \mathrm{V}

The same data and graph points were assessed in (9702/41/O/N/25 Q5(b)).