Electric fields
Apply Coulomb’s law, electric fields and potential to charges, particle motion and capacitor energy in H2 Physics.
Offline pages
Saved on this device only. Connect at least once every 30 days to confirm Premium. Sign-out or a change of account removes saved copies.
Before you begin
Charges push and pull on each other without touching. The lessons start with Coulomb’s law for the force between two point charges, then describe the space around a charge in two ways: as a field strength, the force per unit charge, and as a potential, the energy per unit charge. Linking the two through the potential gradient leads to the uniform field between parallel plates, the motion of charged particles in it, and the energy stored in a capacitor.
Be comfortable with: gravitational fields, because field strength, potential and potential energy are defined the same way there.
Learning goals
- Apply Coulomb's law to the force between point charges.
- Define electric field strength and calculate resultant fields due to point charges.
- Define electric potential and calculate potential due to point charges.
- Relate electric potential, potential energy and work for systems of point charges.
- Use the negative potential gradient and relate equipotentials to field lines.
- Calculate field strength and force in uniform electric fields.
- Analyse charged-particle motion in uniform electric fields.
- Apply capacitance and capacitor-energy relationships.
Syllabus statements covered
- recall and use Coulomb’s law in the form F = Q₁Q₂/(4πε₀r²) for the electric force between two point charges in free space or air
- recall and use E = Q/(4πε₀r²) for the electric field strength due to a point charge, in free space or air, to solve problems
- define electric potential at a point as the work done per unit charge by an external force in bringing a small positive test charge from infinity to that point
- use the equation V = Q/(4πε₀r) for the electric potential in the field due to a point charge, in free space or air
- show an understanding that the electric potential energy of a system of two point charges is Uᴱ = Q₁Q₂/(4πε₀r)
- recall that electric field strength at a point is equal to the negative potential gradient at that point and use this to solve problems
- calculate the field strength of the uniform electric field between charged parallel plates in terms of the potential difference and plate separation
- calculate the force on a charge in a uniform electric field
- describe the effect of a uniform electric field on the motion of a charged particle
- define capacitance as the ratio of the charge stored to the potential difference and use C = Q/V to solve problems
- recall that the electric potential energy stored in a capacitor is given by the area under the graph of potential difference against charge stored, and use this and the equations U = ½QV, U = ½Q²/C and U = ½CV² to solve problems
Lessons
Work through them in order.
Core lessons
- Coulomb force between point chargesUse Coulomb's law for the force between two point charges, and add the forces from several charges.
- Electric field strength due to a point chargeDefine electric field strength, calculate the field of a point charge, and add fields to find resultants and neutral points.
- Electric potential, pair energy and workDefine electric potential, and calculate potentials, the potential energy of two charges and energy changes between two points.
- Reading fields from potential graphs and mapsFind field strength as the negative potential gradient, and read field strength and direction from equipotential maps.
- Uniform fields between parallel platesUse E = V/d between parallel plates and F = qE for the force on a charge in the field.
- Charged particles in a uniform electric fieldPredict the path and speed of a charged particle in a uniform field, using components or energy.
- Capacitance and stored electric potential energyDefine capacitance and calculate the energy a capacitor stores from the area under a V–Q graph.
Practise and check
Or choose
Topic reference
Quick reference
| Idea | Relation | Notes |
|---|---|---|
| Coulomb’s law | F = Q₁Q₂/4πε₀r² | point charges in free space or air |
| field strength | E = F/q | vector; N C⁻¹ = V m⁻¹ |
| field of a point charge | E = Q/4πε₀r² | away from + Q, towards -Q |
| potential of a point charge | V = Q/4πε₀r | scalar; zero at infinity |
| potential energy of two charges | UE = Q₁Q₂/4πε₀r | negative for unlike charges |
| field and potential | E = -dV/dx | field points to lower potential |
| parallel plates | E = V/d | uniform field; force F = qE |
| capacitance | C = Q/V | Q is the charge on either plate |
| energy in a capacitor | U = (1/2)QV = Q²/2C = (1/2)CV² | area under the V–Q graph |
1/4πε₀ = 8.99 × 10⁹ N m² C⁻²
Core knowledge to remember
- Electric field strength at a point is the electric force per unit charge on a positive charge placed at that point.
- Electric potential at a point is the work done per unit charge by an external force in bringing a small positive test charge from infinity to that point.
- The electric field strength at a point is equal to the negative of the potential gradient at that point.
- Field lines cross equipotentials at right angles; closely spaced equipotentials (at equal steps) mean a strong field.
- A charged particle entering a uniform field at right angles to it follows a parabola, with constant velocity across the field and constant acceleration along it.
- Capacitance is the ratio of the charge stored to the potential difference.
Common mistakes
- Squaring r in the potential, or not squaring it in the field.
- Adding fields as numbers, or potentials as vectors.
- Giving the force on an electron the direction of the field.
- Assuming that moving to a higher potential raises the potential energy of every charge; for a negative charge it lowers it.
- Using E = Q/4πε₀r² between parallel plates instead of E = V/d.
- Writing the energy stored in a capacitor as QV instead of (1/2)QV.