6.2FieldsCore

Coulomb’s Law and Electric Field Strength

Swap mass for charge in Newton’s law of gravitation and you get Coulomb’s law — the same inverse-square pattern, but now capable of both pushing and pulling, since charge (unlike mass) comes in two signs.

40 min Video by DrPhysicsA Module 6.2 Electric fields

Electric Fields — A Level PhysicsWatch the full walkthrough before the notes below.

Open on YouTube

What you'll be able to do

Use Coulomb’s law for the force between two point charges
Define electric field strength
Calculate electric field strength for a point charge (radial field)
Calculate electric field strength between parallel plates (uniform field)

Coulomb’s law

Coulomb’s law states the electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation — attractive for opposite charges, repulsive for like charges.

F = \frac{Qq}{4 π ε _{0} r ^{2}}

Coulomb’s law; ε₀ = 8.85 × 10⁻¹² F m⁻¹.

1Use

F = \frac{Qq}{4 π ε _{0} r ^{2}}

F = \frac{4.0 \times 1 0 ^{- 6} \times 1.5 \times 1 0 ^{- 6}}{4 π \times 8.85 \times 1 0 ^{- 12} \times 0.6 0 ^{2}}

Answer

F \approx 0.150

N, attractive

Electric field strength

Electric field strength, $E$ , is the force per unit positive charge at a point. Around an isolated point charge, the field is radial, following an inverse-square law; between charged parallel plates, the field is uniform.

E = \frac{F}{Q} = \frac{Q}{4 π ε _{0} r ^{2}} E = \frac{V}{d}

Electric field strength (radial and uniform cases).

1Use

E = \frac{Q}{4 π ε _{0} r ^{2}}

E = \frac{6.0 \times 1 0 ^{- 9}}{4 π \times 8.85 \times 1 0 ^{- 12} \times 0.3 0 ^{2}}

Answer

E \approx 599

N C⁻¹

Tip — Field between parallel plates is UNIFORM (same everywhere), while field around a point charge follows an inverse-square law — don’t mix the two formulas up.

Equation recap

F = \frac{Qq}{4 π ε _{0} r ^{2}}

Coulomb’s law.

E = \frac{Q}{4 π ε _{0} r ^{2}}

Electric field strength (radial).

E = \frac{V}{d}

Electric field strength (uniform).

Common mistakes to avoid

Forgetting electric force can be repulsive as well as attractive.

Like charges repel; unlike charges attract — check signs before deciding direction.

Using the radial-field formula for parallel plates.

Between plates the field is uniform; use E=V/d, not the point-charge formula.

Key takeaways

Coulomb’s law: F = Qq/(4πε₀r²).
Electric field strength E = F/Q; radial around a point charge (E=Q/4πε₀r²), uniform between plates (E=V/d).

Test yourself

Ready to lock in Coulomb’s Law and Electric Field Strength? Pick a mode and earn XP & Dobloons.