Quick answer: An electric field is the region around a charge where other charges feel a force, with strength is E = F / q in N/C. Coulomb’s law gives the force between point charges: F = kQ₁Q₂ / r². Between plates E = V / d is uniform, and a charge moving through a potential difference ΔV gains energy qΔV.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB D.2
What is an electric field?
Every electric charge changes the space around it. Another charge placed there feels a force, and the map of that influence is the electric field. Also, a rubbed balloon sticking to a wall and a lightning flash both come from such fields.
Electric field strength E at a point equals the force per unit positive charge there: E = F / q. It is a vector, so we give it in newtons per coulomb (N/C), which equals volts per metre (V/m).
How does Coulomb’s law give the force between charges?
Two point charges attract if their signs differ and repel if they are the same. The force falls with the square of the distance, just as gravity does, but it is far stronger.
F = kQ₁Q₂ / r² and, for a point charge, E = kQ / r²
F = force (N), E = field strength (N/C), Q = charge (C), r = distance between centres (m), k = 1 / (4πε₀) = 8.99 × 10⁹ N m²/C². In addition, the elementary charge is e = 1.60 × 10⁻¹⁹ C.
A +3.0 nC charge and a −5.0 nC charge are 4.0 cm apart. Calculate the force between them.
F = kQ₁Q₂ / r² = (8.99 × 10⁹ × 3.0 × 10⁻⁹ × 5.0 × 10⁻⁹) / (0.040)² = 1.35 × 10⁻⁷ / 1.6 × 10⁻³ = 8.4 × 10⁻⁵ N, and it is attractive because the signs differ.
Put r in metres, not centimetres, and square it. Students most often forget to convert 4.0 cm to 0.040 m, so their answer is wrong by a factor of 10⁴.
What is the field between two charged plates?
Two parallel metal plates connected to a power supply create a uniform field. The field lines are parallel and equally spaced, so E has the same size and direction everywhere between the plates, except near their edges.
For plates separated by a distance d with potential difference V: E = V / d. A charge q feels a constant force F = qE, so a free particle accelerates uniformly and follows a parabola if it enters at right angles to the field.
Plates 2.0 cm apart have a potential difference of 600 V. Calculate the field and the acceleration of an electron.
E = V / d = 600 / 0.020 = 3.0 × 10⁴ V/m. F = eE = 1.60 × 10⁻¹⁹ × 3.0 × 10⁴ = 4.8 × 10⁻¹⁵ N. a = F / m = 4.8 × 10⁻¹⁵ / 9.11 × 10⁻³¹ = 5.3 × 10¹⁵ m/s².
How do potential and energy work in an electric field?
Electric potential V is the work per unit positive charge that you do to bring a small test charge from infinity to a point. Around a point charge, V = kQ / r. Potential is a scalar, so contributions from several charges simply add with their signs.
| Quantity | Point charge | Uniform field |
|---|---|---|
| Field strength | E = kQ / r² (falls as 1/r²) | E = V / d (constant) |
| Potential | V = kQ / r (falls as 1/r) | V changes linearly with distance |
| Force on charge q | F = qE, radial | F = qE, constant |
| Link | E = −ΔV / Δr | E = −ΔV / Δx |
Energy gained by a charge in an electric field
When a charge q moves through a potential difference ΔV, the field does work W = qΔV. For an electron or proton the convenient unit is the electronvolt: 1 eV = 1.60 × 10⁻¹⁹ J, the energy gained by a charge e crossing 1 V.
A 500 V potential difference accelerates an electron from rest. Calculate its speed.
Gain in kinetic energy = eV = 500 eV = 8.0 × 10⁻¹⁷ J. From ½mv² = eV, v = √(2eV / m) = √(2 × 8.0 × 10⁻¹⁷ / 9.11 × 10⁻³¹) = 1.3 × 10⁷ m/s.
Sketch the field lines and mark the direction of the force on a positive charge first. For an electron, reverse the arrow. Most sign errors disappear after that sketch.
- E = F / q, measured in N/C or V/m
- Coulomb’s law: F = kQ₁Q₂ / r², with k = 8.99 × 10⁹ N m²/C²
- Point charge: E = kQ / r² and V = kQ / r
- Uniform field between plates: E = V / d and F = qE
- Energy gained by a charge crossing ΔV is qΔV; 1 eV = 1.60 × 10⁻¹⁹ J
Charges, Coulomb’s law and electric potential: frequently asked questions
What is the unit of electric field strength?
The unit is newton per coulomb (N/C), which is identical to volt per metre (V/m). Use N/C when you think about force and V/m when you think about potential difference across a gap.
How does the electric force change if the distance doubles?
The force falls to one quarter because Coulomb’s law is an inverse square law. Moreover, the same rule applies to the field strength of a point charge.
Why is the field between parallel plates uniform?
Charge spreads evenly over the large flat plates, so the field lines run parallel and equally spaced from one plate to the other. Similarly, only near the edges do the lines bulge outwards.
What is an electronvolt?
It is the energy that one elementary charge gains when it moves through a potential difference of one volt. Also, it equals 1.60 × 10⁻¹⁹ J and we use it for particles such as electrons.
How do electric and gravitational fields differ?
Gravity always attracts, but electric forces can attract or repel because charge has two signs. In addition, the electric force between two protons is about 10³⁶ times larger than their gravitational attraction.
