OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(b) electric potential V = Q/(4πε₀r) at a distance r from a point charge;…
Full specification wording
Electric potential and energy: (b) electric potential V = Q/(4πε₀r) at a distance r from a point charge; changes in electric potential
Electric potential at a point is the work done per unit positive charge in bringing a small positive test charge from infinity to that point.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 2 of 5
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Electric potential at a point is the work done per unit positive charge in bringing a small positive test charge from infinity to that point. For a point charge Q, V = Q/(4πε₀r), where r is the distance from the centre of Q and ε₀ = 8.85 × 10⁻¹² F m⁻¹. Potential is a scalar, so potentials from several charges add algebraically, keeping signs. A positive Q gives positive V; a negative Q gives negative V. Moving between two points changes potential by ΔV = V_final − V_initial, and the work done on a charge q is qΔV. Example: for Q = +2.0 × 10⁻⁹ C at r = 0.30 m, V = (2.0 × 10⁻⁹)/(4π × 8.85 × 10⁻¹² × 0.30) ≈ 60 V.
What earns the marks
- States that electric potential is work done per unit positive charge brought from infinity to the point.
- Uses V = Q/(4πε₀r) with ε₀ = 8.85 × 10⁻¹² F m⁻¹ and r measured from the centre of the point charge.
- Recognises V is a scalar and adds potentials algebraically, retaining the sign of each charge.
- Calculates a change in potential as ΔV = V_final − V_initial and links it to work done per unit charge.
- Keeps the correct sign: positive Q gives positive V, negative Q gives negative V.
Common mistakes and how to put them right
Treating potential as a vector and adding components.
Put it right: Potential is a scalar, so values are added algebraically with their signs.
Measuring r from the surface of a charged sphere rather than from its centre.
Put it right: For an external point, r is the distance from the centre.
Confusing electric potential V with electric potential energy.
Put it right: V is energy per unit charge, measured in J C⁻¹ or V.
Forgetting the sign of Q when substituting.
Put it right: A negative charge gives a negative potential at every finite distance.
Exam tips
- Write the equation, substitute values with units, then evaluate; show the power-of-ten handling clearly.
- Check whether the question asks for potential at a point or a change in potential between two points before calculating.
- Use ε₀ = 8.85 × 10⁻¹² F m⁻¹ and keep at least three significant figures through the working.
Try the lesson
The start of the Electric potential and energy: (b) electric potential V = Q/(4πε₀r) at a distance r from a point charge; changes in electric potential lesson, made from checked teaching notes for this specification point.
Listen
Electric potential at a point is the work done per unit positive charge in bringing a small positive test charge from infinity to that point. For a point charge Q, V = Q/(4πε₀r), where r is the distance from the centre of Q and ε₀ = 8.85 × 10⁻¹² F m⁻¹. Potential is a scalar, so potentials from several charges add algebraically, keeping signs. A positive Q gives positive V; a negative Q gives negative V. Moving between two points changes potential by ΔV = V_final − V_initial, and the work done on a charge q is qΔV. Example: for Q = +2.0 × 10⁻⁹ C at r = 0.30 m, V = (2.0 × 10⁻⁹)/(4π × 8.85 × 10⁻¹² × 0.30) ≈ 60 V. A strong answer earns marks for these points. States that electric potential is work done per unit positive charge brought from infinity to the point. Uses V = Q/(4πε₀r) with ε₀ = 8.85 × 10⁻¹² F m⁻¹ and r measured from the centre of the point charge. Recognises V is a scalar and adds potentials algebraically, retaining the sign of each charge. Calculates a change in potential as ΔV = V_final − V_initial and links it to work done per unit charge. Exam tip: Write the equation, substitute values with units, then evaluate; show the power-of-ten handling clearly.
Key words
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Electric potential
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Inverse relationship between potential and distance
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Scalar nature of potential and algebraic addition
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Sign convention for positive and negative charges
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See every definition
- Electric potential
- The work done per unit positive charge in bringing a small positive test charge from infinity to that point.
- Inverse relationship between potential and distance
- For a point charge Q, V = Q/(4πε₀r), where r is the distance from the centre of Q and ε₀ = 8.85 × 10⁻¹² F m⁻¹.
- Scalar nature of potential and algebraic addition
- Potential is a scalar, so potentials from several charges add algebraically, keeping signs.
- Sign convention for positive and negative charges
- A positive Q gives positive V; a negative Q gives negative V.
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