Fields and potential-energy change
Key idea: H2 Physics lessons on energy stores, work, kinetic and potential energy, fields, power and efficiency.
Continue where you stopped
The core idea
Build the idea
Learn the idea
Big question: How do field lines and equipotentials turn an invisible interaction into a map?
Field strength describes force per unit test property; potential describes potential energy per unit test property. Field lines show the force direction on a positive test object, while equipotentials join equal potential and meet field lines at right angles. Moving along an equipotential requires no field work; moving across potential changes the system's potential energy.
Define a field using a small test object
A field is a region where a suitable body may experience force. Gravitational field strength is force per unit mass; electric field strength is force per unit positive charge. The source creates the field whether or not a test body is present.
Field lines point in the force direction for a positive test mass or positive test charge. A negative charge experiences force opposite to the electric-field direction.
Check your understanding: Does removing a positive test charge remove the electric field?
No. The source charges create the field; the test charge only reveals it through force.
Read field lines and equipotentials together
Parallel equally spaced lines represent a uniform field; radial lines represent a field whose direction and strength vary with position. Field lines never cross, and closer spacing represents greater field strength qualitatively.
Equipotential surfaces meet field lines at right angles. Moving along an equipotential changes no potential energy, while moving across equipotentials can transfer energy between the field-related potential store and other stores.
Check your understanding: Why is no field work done along an equipotential?
There is no potential difference along it, and the displacement is perpendicular to the field force.
Connect field work to potential-energy change
When a field does positive work, the corresponding potential energy decreases: Wfield = −ΔEp. Work done by an external force against the field can increase potential energy.
Always identify the system and the sign of the test mass or charge. The same electric-field direction produces opposite force directions for positive and negative charges.
Check your understanding: A field does +3.0 J of work. What is ΔEp?
ΔEp = −3.0 J.
Key ideas to keep
- Closer field lines represent a stronger field; they never cross.
- Potential is a scalar even though field strength is a vector.
- A negative gradient links field strength to potential, so the field points toward decreasing potential.
See the reasoning
Worked example
Track force, work and energy for a negative charge
Question: An electron moves 0.080 m opposite to a uniform electric field of 3.0 × 10⁴ N C⁻¹. Find the work done by the field and the electric potential-energy change. Use e = 1.60 × 10⁻¹⁹ C.
Step 1: Find the force
Why: The electron's negative charge reverses the field direction.
Working: Force magnitude = eE = 4.8 × 10⁻¹⁵ N, opposite E.
Step 2: Compare force and displacement
Why: The electron moves opposite E, which is along its force.
Working: Wfield = Fs = (4.8 × 10⁻¹⁵)(0.080) = 3.84 × 10⁻¹⁶ J.
Step 3: Find the store change
Why: Positive field work reduces the associated potential-energy store.
Working: ΔEp = −Wfield = −3.84 × 10⁻¹⁶ J.
Answer: The field does +3.84 × 10⁻¹⁶ J of work and electric potential energy decreases by 3.84 × 10⁻¹⁶ J.
Check: The electron accelerates along its force, so a potential-energy decrease can become kinetic energy.
Another worked model
Question
A positive charge moves along a uniform electric field and its potential energy changes by −4.8 × 10⁻¹⁶ J. Find field work and explain the force direction.
Check the worked solution
A positive charge experiences force along the field lines. W_field = −ΔU = +4.8 × 10⁻¹⁶ J, consistent with displacement along the force.
Use a hint if needed
Practise with support
Try this
A 2.0 kg mass experiences 19.6 N downward. Calculate g and state the direction of the gravitational field.
Hint: Use the defining ratio.
Check your answer
g = F/m = 19.6/2.0 = 9.8 N kg⁻¹ downward, along the gravitational field lines.
Now work without the hint
Practise independently
Your turn
Compare uniform and radial fields, define both gravitational and electric field strength, and state the relationship between field work and potential-energy change.
Check your answer
Uniform fields have parallel equally spaced lines; radial lines converge on or diverge from a centre. g = F/m and E = F/q for a positive test charge. Equipotentials are perpendicular to field lines and W_field = −ΔU.
Avoid these traps
Common mistakes
Common mistake
A field exists only when a test body is present.
What is wrong with this reasoning?
Show better thinking
A source establishes the field. A test mass or positive test charge only defines its strength and direction.
Common mistake
Positive work by a field increases potential energy.
What is wrong with this reasoning?
Show better thinking
Work done by a field is W_field = −ΔU, so positive field work corresponds to decreasing potential energy.
Write for the examiner
Exam guidance
State the sign of the test mass or charge before inferring force or energy change from a field diagram.
Exam-style practice [7 marks]
Sketch field lines and equipotentials between oppositely charged parallel plates. A negative charge moves from the negative plate towards the positive plate. State the force direction and explain the field work and potential-energy changes.
Plan before you answer
- Draw the uniform field first.
- Add perpendicular equipotentials.
- Use the charge sign before discussing work.
Mark your answer and compare the model
Marking points
Tick each point only if your answer states it clearly.
Model answer
Between the plates, draw straight parallel field lines from the positive plate to the negative plate and equipotentials perpendicular to them. A negative charge feels force opposite E, towards the positive plate. Its displacement is along that force, so the field does positive work and the electric potential energy of the charge–field system decreases.
Come back in three days
Check what stayed with you
Recall question 1
Define electric field strength.
Check the answer
Force per unit positive charge at a point.
Recall question 2
How do equipotentials meet field lines?
Check the answer
At right angles.
Recall question 3
State the field-work relation.
Check the answer
Wfield = −ΔEp.
Syllabus and review details
This lesson covers the listed H2 Physics 9478 outcomes. For this topic, a field is a region where a mass, charge or current-carrying conductor experiences a force. Keep field force, potential energy and power ideas distinct, and state the system whenever you apply conservation of energy.
- GCE A-Level H2 PhysicsTopic 4(f) / Topic 4(g) / Topic 4(h) / Topic 4(i) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027