What is an electric field?
Charges push or pull each other without touching. We explain this with a field: every charge creates an electric field in the space around it, and any other charge in that space feels a force.
To find the field, imagine a very small positive test charge q. It is small so it does not disturb the charges that make the field. A field from charges that do not move is called an electrostatic field.
Electric field strength E = F/q
The electric field strength at a point is the force per unit positive charge placed there:
E = F / q
Unit: newton per coulomb (N/C), which equals volt per metre (V/m). E is a vector: its direction is the direction of the force on a + charge. A − charge feels a force opposite to E.
If you know E, the force on any charge is F = qE. For a point charge Q at distance r (in air or vacuum):
E = kQ / r², where k = 1/(4πε₀) ≈ 9 × 10⁹ N m²/C².
Double the distance → E becomes ¼. Triple → 1/9. This is an inverse-square law.
Electric field lines
- Lines start on + charges and end on − charges (or go to infinity).
- The arrow on a line shows the direction of E at each point; the tangent gives the direction on a curved line.
- Lines close together = strong field; far apart = weak field.
- Lines never cross (E has only one direction at a point).
- A bigger charge has more lines.
Between two flat parallel plates with + and − charge, the lines are straight, parallel and evenly spaced: a uniform field, where E = V/d.
Superposition: many charges
When several charges are present, the total field at a point is the vector sum of the fields from each charge: E = E₁ + E₂ + …
If the two fields point the same way, add their sizes; if opposite, subtract. Otherwise, add them as arrows (head to tail).
A dipole (+q and −q close together) has lines that curve out of + and into −. Midway between two equal like charges the fields cancel, so E = 0 there.
Key formulas and definitions
- E = F / q (unit N/C = V/m)
- F = qE
- Point charge: E = kQ / r², k = 9 × 10⁹ N m² C⁻²
- Uniform field between plates: E = V / d
- Superposition: E_total = E₁ + E₂ + … (vector sum)
Worked examples
1. A charge of 2 × 10⁻⁶ C feels a force of 0.08 N. Find the field strength.
E = F/q = 0.08 / (2 × 10⁻⁶) = 4 × 10⁴ N/C.
2. Find E at 0.1 m from a point charge of 2 µC.
E = kQ/r² = 9 × 10⁹ × 2 × 10⁻⁶ / 0.01 = 1.8 × 10⁶ N/C, pointing away from the charge.
3. The field at 1 m from a charge is 900 N/C. What is it at 3 m?
E ∝ 1/r². Distance × 3 → E ÷ 9 = 100 N/C.
4. An electron (charge 1.6 × 10⁻¹⁹ C) is in a field of 5 × 10³ N/C. Find the force on it and its direction.
F = qE = 1.6 × 10⁻¹⁹ × 5 × 10³ = 8 × 10⁻¹⁶ N, opposite to E because the electron is negative.
5. Two plates 2 cm apart have 200 V between them. Find E.
E = V/d = 200 / 0.02 = 1 × 10⁴ V/m (= N/C).
6. Charges +4 µC and +4 µC are 0.2 m apart. What is E at the midpoint?
Each gives E = kQ/(0.1)² = 3.6 × 10⁶ N/C, but in opposite directions. They cancel: E = 0.
Common mistakes
- Thinking E depends on the test charge. Changing q changes F, but F/q stays the same.
- Using r instead of r² in E = kQ/r².
- Forgetting that E is a vector: fields in opposite directions subtract, they don't add.
- Thinking field lines are real wires or paths. They are a drawing tool; a charge does not always move along them.