Electric potential Cambridge International AS & A Level Physics revision
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In plain words
Pushing a positive charge towards another positive charge is like pushing a ball up a hill: you have to do work, and the charge stores it. Electric potential says how high the hill is at each point, in joules for every coulomb.
4 things to know
- The electric potential V at a point is the work done per unit positive charge in bringing a small test charge from infinity to that point. Units: volts (J/C). It is zero at infinity.
- For a point charge Q: V = Q ÷ 4πε₀r. It is positive near a positive charge and negative near a negative charge. Potential is a scalar.
- The work done in moving a charge q through a potential difference ΔV is qΔV. So the electric potential energy of two point charges Q and q a distance r apart is Qq ÷ 4πε₀r.
- Field strength is minus the potential gradient: E = −ΔV ÷ Δr. The field points from high potential towards low potential.
Worked example
Find the potential 0.20 m from a point charge of +4.0 nC, and the work done in bringing a charge of +2.0 nC from infinity to that point.
- V = Q ÷ 4πε₀r = 8.99 × 10⁹ × 4.0 × 10⁻⁹ ÷ 0.20 = 180 V.
- Work done = qV = 2.0 × 10⁻⁹ × 180.
- = 3.6 × 10⁻⁷ J.
Tips and tricks
- Potential depends on 1 ÷ r. Field strength depends on 1 ÷ r². Don't square r for potential.
- Potentials are scalars, so add them as plain numbers, keeping their signs.
It lands in your notebook with its questions as flashcards.
Electric potential: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
How does the potential due to a point charge depend on the distance r from it?
V = Q ÷ 4πε₀r.
Where is the electric potential due to a point charge zero?
That is how potential is defined.
Is electric potential a scalar or a vector?
It has a sign but no direction.
What is the sign of the electric potential near an isolated negative charge?
The field would do the work of bringing a positive test charge in.
How is electric field strength related to potential?
E = −ΔV ÷ Δr.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
4 questions, 8 marks. Write your answers on paper, then check them.
Electric potential
Cambridge International AS & A Level Physics 9702 · 8 marks · papermunch.org
Name ______________________________ Date ______________
Find the electric potential 0.50 m from a point charge of −6.0 nC.[2]
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−108 V (about −110 V).
A charge of 3.0 µC is moved between two points whose potentials differ by 200 V. Find the work done.[2]
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6.0 × 10⁻⁴ J.
Charges of +3.0 nC and −3.0 nC are placed a short distance apart. State the potential at the point midway between them, and explain your answer.[2]
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Zero. The potentials due to the two charges are equal in size with opposite signs, and potentials add as scalars.
In a uniform electric field the potential falls by 60 V over a distance of 0.030 m. Find the field strength.[2]
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2000 V/m.
Answers: Electric potential
- 1. −108 V (about −110 V).
- 2. 6.0 × 10⁻⁴ J.
- 3. Zero. The potentials due to the two charges are equal in size with opposite signs, and potentials add as scalars.
- 4. 2000 V/m.