OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(d) force–distance graph for a point or spherical charge; work done is…
Full specification wording
Electric potential and energy: (d) force–distance graph for a point or spherical charge; work done is area under graph
The electrostatic force between two point charges follows an inverse-square law, F = Qq/(4πε₀r²), so a force–distance graph is a curve that falls steeply as r increases and never crosses the axis…
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 4 of 5
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The electrostatic force between two point charges follows an inverse-square law, F = Qq/(4πε₀r²), so a force–distance graph is a curve that falls steeply as r increases and never crosses the axis for like charges. The work done moving a charge between two separations equals the area under the force–distance graph between those limits. Because the curve is not linear, the area must be found by integration or by counting squares, not by treating the graph as a triangle.
For example: Moving a charge from r = 0.10 m to r = 0.20 m requires the area between those values, which equals the change in electric potential energy.
What earns the marks
- States that the electrostatic force between point charges obeys F = Qq/(4πε₀r²), an inverse-square relationship.
- Describes the force–distance graph as a curve decreasing with distance, asymptotic to the distance axis.
- States that work done equals the area under the force–distance graph between the two separations.
- Recognises that the area must be found by integration or square-counting because the graph is curved.
- Links the area under the graph to the change in electric potential energy between the two positions.
Common mistakes and how to put them right
Treating the curve as a straight line and using a triangle area.
Put it right: The inverse-square curve requires integration or square-counting.
Using the force at one separation as a constant force across the whole distance.
Put it right: Force varies continuously with r.
Forgetting that work done is the area between two specific limits, not the total area from zero to infinity.
Mixing up the force–distance graph with the potential–distance graph, which has a different shape and meaning.
Exam tips
- Sketch the curve first, mark the two limits on the distance axis, and shade the area you need to find.
- If counting squares, state the area of one square in J and multiply by the number of squares counted.
- Check the sign of the work done: moving like charges closer together requires positive work by an external agent.
Try the lesson
The start of the Electric potential and energy: (d) force–distance graph for a point or spherical charge; work done is area under graph lesson, made from checked teaching notes for this specification point.
Listen
The electrostatic force between two point charges follows an inverse-square law, F = Qq/(4πε₀r²), so a force–distance graph is a curve that falls steeply as r increases and never crosses the axis for like charges. The work done moving a charge between two separations equals the area under the force–distance graph between those limits. Because the curve is not linear, the area must be found by integration or by counting squares, not by treating the graph as a triangle. For example, moving a charge from r = 0.10 m to r = 0.20 m requires the area between those values, which equals the change in electric potential energy. A strong answer earns marks for these points. States that the electrostatic force between point charges obeys F = Qq/(4πε₀r²), an inverse-square relationship. Describes the force–distance graph as a curve decreasing with distance, asymptotic to the distance axis. States that work done equals the area under the force–distance graph between the two separations. Recognises that the area must be found by integration or square-counting because the graph is curved. Exam tip: Sketch the curve first, mark the two limits on the distance axis, and shade the area you need to find.
Key words
Say what each word means before you turn the card.
Inverse-square law for electrostatic force
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Graphical representation of force against distance
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Work done as area under a force–distance graph
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Relationship between work done and potential energy change
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See every definition
- Inverse-square law for electrostatic force
- The electrostatic force between point charges obeys F = Qq/(4πε₀r²), an inverse-square relationship.
- Graphical representation of force against distance
- A curve decreasing with distance, asymptotic to the distance axis, that falls steeply as r increases and never crosses the axis for like charges.
- Work done as area under a force–distance graph
- Work done equals the area under the force–distance graph between the two separations, found by integration or square-counting because the graph is curved.
- Relationship between work done and potential energy change
- The area under the graph between two positions equals the change in electric potential energy between those positions.
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