Define electric fields and read field lines
Define electric field strength as force per unit positive charge and use field-line direction and spacing to interpret a field.
Section 18 · Electric fields
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 18. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use force, charge, work, energy, potential difference, inverse-square relationships and SI units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Electric field direction at a point is defined using which test charge?
What you will learn
- Define an electric field as a field of force
- Define field strength as force per unit positive charge
- Use F = qE and represent electric fields with field lines
A field describes the force a charge would experience
An electric field is a region where a charged particle experiences an electric force. At a point, electric field strength E is the force per unit positive test charge: E = F/q for a positive test charge. Its direction is the direction of force on a positive charge, and its unit is N C⁻¹ (equivalently V m⁻¹).
For a charge q placed in a field, F = qE. A positive q experiences force along E; a negative q experiences force opposite E. The equation is vectorial: when calculating magnitudes, use |F| = |q|E and state the direction separately.
Field lines show direction and relative strength
Electric field lines point in the direction a positive test charge would move. They leave positive charges and enter negative charges. Around an isolated point charge they are radial; between oppositely charged parallel plates, the central region is approximately uniform and the lines are parallel.
Closer field lines represent a stronger field in a qualitative diagram. Lines do not cross, because the field at one point cannot point in two different directions. Field lines are a representation of the field, not paths that every charged particle must follow.
Pause and explain
A negative charge is placed in an electric field pointing north. Which way is its force?
Worked example
A charge of +2.0 μC is placed in an electric field of 3.0 × 10⁴ N C⁻¹ directed east. Find the force on it.
Show the worked solution
- Use F = qE.
- Convert 2.0 μC to 2.0 × 10⁻⁶ C.
- A positive charge's force follows the field direction.
Answer F = 2.0 × 10⁻⁶ × 3.0 × 10⁴ = 6.0 × 10⁻² N east.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A +4.0 μC charge is in a uniform field of 1.5 × 10⁴ N C⁻¹. Calculate the force magnitude and direction relative to the field.
Give me a hint
Use F = qE and convert microcoulombs to coulombs.
Compare my reasoning
- q = +4.0 × 10⁻⁶ C.
- F = qE = 4.0 × 10⁻⁶ × 1.5 × 10⁴ = 6.0 × 10⁻² N.
- The positive charge's force is along the field.
6.0 × 10⁻² N along the field.
Look for these in your work
- Charge converted
- Product calculated
- Direction stated
An electron is in a field directed vertically downward. State the direction of its electric force and explain.
Give me a hint
An electron has negative charge, so use the field direction for a positive charge as the reference.
Compare my reasoning
- The field points in the direction of force on a positive charge.
- An electron has negative charge.
- Its force is opposite to the field, so it is vertically upward.
The electron's electric force is vertically upward, opposite the downward field.
Look for these in your work
- Positive-charge convention recalled
- Electron sign used
- Opposite direction stated
Describe two rules for sketching field lines around an isolated positive charge and an isolated negative charge.
Give me a hint
Use the field direction for a positive test charge and the radial symmetry of a point charge.
Compare my reasoning
- Lines around an isolated point charge are radial.
- They point outward from a positive charge and inward towards a negative charge.
- Line density can indicate relative field strength; lines must not cross.
Draw radial lines outward from + and inward to −; use spacing to show relative strength and never let lines cross.
Look for these in your work
- Radial pattern stated
- Directions for both signs correct
- Density and non-crossing rule included
Common mistakes
- Defining field direction as the force on a negative charge
- Ignoring that F changes direction when q is negative
- Treating field lines as actual particle paths
- Drawing crossing field lines
What can you explain now?
Electric field direction at a point is defined using which test charge?
Compare with the explanation
A positive test charge
The field points in the direction of force on a positive charge.
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Make it stick
How do field direction and force direction differ for a negative charge?
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