Electric Fields & Potential

Coulomb's law, field strength, uniform and radial fields, electric potential, and comparison with gravitational fields.

Spec Points Covered
  • State CoulombThe SI unit of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. One coulomb is the chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). transferred by a current of 1 A in 1 second.'s law and apply it to calculate the force between point charges.
  • Define electric field strengthThe force per unit positive chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). at a point in an electric field. Measured in N C⁻¹ or V m⁻¹. and distinguish between its two expressions ($E = F/Q$ and $E = V/d)$.
  • Calculate the electric field strengthThe force per unit positive charge at a point in an electric field. Measured in N C⁻¹ or V m⁻¹. due to a point charge using $E = Q / (4piepsilon0 r^2)$.
  • Describe the motion of charged particles in uniform electric fields.
  • Define electric potentialThe work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (charge times potential difference). per unit positive charge in bringing a small test charge from infinity to that point. and calculate it for a point charge using $V = Q / (4piepsilon0 r)$.
  • Relate electric field strengthThe force per unit positive charge at a point in an electric field. Measured in N C⁻¹ or V m⁻¹. to potential gradient: $E = -DeltaV / Deltar$.
  • Calculate work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (charge times potential difference). when a charge moves through a potential differenceThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V)..
  • Compare and contrast electric and gravitational fields.
Notes
01 Coulomb's law gives the force between two point charges Coulomb's law 3.7.3.1 → 02 A charged sphere acts as a point charge for an external observer 3.7.3.1 → 03 Electric field lines show direction and strength 3.7.3.2 → 04 Electric field strength is force per unit charge Electric field strength 3.7.3.2 → 05 Uniform field between parallel plates: E = V/d $E = \frac{V}{d}$ 3.7.3.2 → 06 Charged particles follow parabolic paths between parallel plates 3.7.3.2 → 07 Radial field strength follows an inverse square law $E = \frac{Q}{4\pi\varepsilon_0 r^2}$ 3.7.3.2 → 08 Electric potential is the work done per unit charge from infinity Electric potential 3.7.3.3 → 09 Combining electric potentials: just add them 3.7.3.3 → 10 The potential gradient links field strength to potential Potential gradient 3.7.3.3 → 11 Work done on a charge equals qDeltaV $\Delta W = q \Delta V$ 3.7.3.3 → 12 Equipotential surfaces are perpendicular to field lines Equipotential surface 3.7.3.3 → 13 Electric and gravitational fields share structure but differ in sign 3.7.3.1 → 14 Worked example: Coulomb's law with an alpha particle and gold nucleus 3.7.3.1 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
Coulomb's law
$$F = \frac{Q_1 Q_2}{4\pi\varepsilon_0 r^2}$$
  • Where:
    • $F$ = electrostatic force (N)
    • $Q_1, Q_2$ = charges (C)
    • $r$ = separation (m)
    • $varepsilon_0$ = permittivity of free space (F m^-1)
Positive F = repulsion (like charges). Negative F = attraction (unlike charges). r is centre-to-centre.
Field strength from potential gradient
$$E = -\frac{\Delta V}{\Delta r}$$
  • Where:
    • $E$ = electric field strength (V m^-1)
    • $DeltaV$ = potential difference (V)
    • $Deltar$ = displacement in field direction (m)
Negative sign: field points towards lower potential. Gradient of V-r graph = E.
Electric field strength (general)
$$E = \frac{F}{Q}$$
  • Where:
    • $E$ = electric field strength (N C^-1)
    • $F$ = force (N)
    • $Q$ = charge (C)
Defines E. Works for any field shape.
Uniform field between parallel plates
$$E = \frac{V}{d}$$
  • Where:
    • $E$ = electric field strength (V m^-1)
    • $V$ = potential difference (V)
    • $d$ = plate separation (m)
Only for uniform fields between parallel plates. Not for point charges.
Radial field strength (point charge)
$$E = \frac{Q}{4\pi\varepsilon_0 r^2}$$
  • Where:
    • $E$ = electric field strength (N C^-1)
    • $Q$ = source charge (C)
    • $r$ = distance from centre (m)
Follows an inverse square law. E-r graph is a 1/\(r^{2}\) curve.
Electric potential (point charge)
$$V = \frac{Q}{4\pi\varepsilon_0 r}$$
  • Where:
    • $V$ = electric potential (V)
    • $Q$ = source charge (C)
    • $r$ = distance from centre (m)
Positive Q gives positive V. Negative Q gives negative V. V = 0 at infinity.
Work done on a charge
$$\Delta W = q \Delta V$$
  • Where:
    • $DeltaW$ = work done (J)
    • $q$ = charge being moved (C)
    • $DeltaV$ = potential difference (V)
q is the charge being moved, not the charge producing the field.
Electric potential energy of two point charges
$$E_p = \frac{Q_1 Q_2}{4\pi\varepsilon_0 r}$$
  • Where:
    • $E_p$ = electric potential energy (J)
    • $Q_1, Q_2$ = charges (C)
    • $r$ = separation (m)
Positive for like charges (repulsion). Negative for unlike charges (attraction). E_p = 0 at infinity.
Q Retrieval Practice All 14 Questions →
Q1. State Coulomb's lawThe electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them..
The electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of their separation: F = Q1Q2 / (4piepsilon0 \(r^{2}\)).
Q2. What is the difference between attractive and repulsive electric forces in terms of charge signs?
  • Like charges (both positive or both negative) repel: Q1Q2 > 0, force is positive.
  • Opposite charges attract: Q1Q2 < 0, force is negative.
Q3. Define electric field strength and state its two equivalent units.
  • The force per unit charge experienced by a small positive test charge placed at that point.
  • Units: N C^-1 or V m^-1.
Q4. Write the expression for electric field strength in a uniform field between parallel plates.
  • E = V/d, where V is the potential differenceThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). and d is the plate separation.
  • Only valid for parallel plates.
Q5. Write the expression for electric field strength due to a point charge.
  • E = Q / (4piepsilon0 \(r^{2}\)).
  • This follows an inverse square law.