Electric Fields
18. Electric Fields
5 min read 10 parts Lesson 1 of 1
Lesson summary
18. Electric Fields — Cambridge AS & A Level Physics 9702 — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes: Describe and sketch electric fields, use F = qE, E = V/d, Coulomb's law, the point-charge field, potential and potential energy equations, and compare them with…
- Electric field strength E
- Force on a charge
- Drawing rules
- Derivation
- Limitation
- Entering perpendicular to the field
Part 1 of 10Electric field and field strength
- Electric field = a region of space in which a charge experiences a force.
- Electric field strength E = the force per unit charge on a small stationary positive test charge, E = F/q, in N C−1 (equivalent to V m−1).
- Direction — E is a vector pointing away from positive charge and towards negative charge, because a positive test charge defines it.
- Force on a charge — F = qE.
- A positive charge feels a force along the field.
- A negative charge feels a force of the same size against the field.
Part 2 of 10Field line patterns
| Field | Line pattern | Field strength |
|---|---|---|
| Uniform | Equally spaced parallel lines | Same size and direction everywhere |
| Radial (point charge) | Straight lines out of a positive charge or into a negative charge | Falls with distance; stronger where lines are closer |
| Charged conducting sphere | Same as a point charge at the centre; lines meet the surface at 90° | Treated like a point charge outside the sphere |
| Two opposite charges | Lines from the positive to the negative charge | Strong attraction when close |
| Two like charges | Lines leave (or enter) both and do not join them; a neutral point lies midway | Strong repulsion when close |
| Parallel plates | Uniform between the plates, curved and non-uniform beyond the edges | Constant between the plates |
- Drawing rules — add arrows, make lines touch the source charge or plate, and never let lines cross.
Part 3 of 10Uniform field between parallel plates
- Equation — E = V/d, with V the potential difference between the plates and d their separation.
- A larger V gives a stronger field and a larger d a weaker field.
- The field points from the positive plate to the negative plate, and an earthed plate is at 0 V.
- Derivation — work on a charge moving between plates is W = Fd = qV, so E = F/q = V/d.
- Limitation — E = V/d applies only to parallel plates, not to the radial field of a point charge.
Part 4 of 10Charged particles in a uniform field
- At rest — a charge moves along the field line, in the field direction if positive and opposite if negative.
- Entering perpendicular to the field — it feels a constant force and follows a parabola, like a projectile in gravity.
- A positive charge curves towards the negative plate and a negative charge towards the positive plate.
- An uncharged particle such as a neutron passes through undeflected.
| Factor | Effect on deflection |
|---|---|
| Greater charge | More deflection (larger force) |
| Greater mass | Less deflection (smaller acceleration) |
| Greater speed | Less deflection (less time between the plates) |
Part 5 of 10Coulomb's law
- Coulomb's law = the 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/(4πε0r2), where r is the distance between centres.
- Permittivity of free space — ε0 = 8.85 × 10−12 F m−1, and air has the same value.
- Other materials have a larger permittivity, which reduces the force.
- Alternative form — F = kQ1Q2/r2 with k = 1/(4πε0) = 8.99 × 109 N m2 C−2.
- Direction — like charges repel (positive product) and unlike charges attract (negative product).
- Validity — it applies to point charges or small charged spheres much smaller than their separation, not irregular charge distributions.
- Spherical conductor — outside it the charge acts as if concentrated at the centre, so the field lines match those of a point charge.
Part 6 of 10Electric field of a point charge
- Equation — E = Q/(4πε0r2), from Coulomb's law divided by the test charge q.
- Behaviour — E follows an inverse square law and is not constant, and it is zero inside a charged conducting sphere.
- Several charges — field strengths add as vectors.
- Along a line, add if in the same direction and subtract if opposite.
- At right angles, use Pythagoras for the magnitude and trigonometry for the direction.
- Method — treat the point as a positive test charge, so the field points away from positive and towards negative sources.
Part 7 of 10Comparison with gravitational fields
| Feature | Gravitational | Electric |
|---|---|---|
| Source | Mass | Charge |
| Force law | F = Gm1m2/r2 | F = Q1Q2/(4πε0r2) |
| Nature of force | Always attractive | Attractive or repulsive |
| Field strength of a point source | GM/r2 | Q/(4πε0r2) |
| Potential | −GM/r (always negative) | Q/(4πε0r) (sign of the charge) |
Part 8 of 10Electric potential
1Electric potential1 point
= the work done per unit charge in bringing a small positive test charge from infinity to the point, in J C−1 or V.
- It is a scalar, zero at infinity, with the sign of the source charge.
2Point charge3 points
— V = Q/(4πε0r), and the same equation applies outside a charged sphere.
- Around a positive charge V is positive and rises as a positive test charge moves closer.
- Around a negative charge V is negative and falls as a positive test charge moves closer.
- Inside a charged conducting sphere the potential is constant.
3Combining charges
— potentials add as scalars.
4Direction
— potential decreases in the direction of the field lines.
Part 9 of 10Potential gradient
- Potential gradient = the rate of change of potential with displacement in the direction of the field.
- Field strength — E = −ΔV/Δr, the negative of the potential gradient.
- Graphs — on a V–r graph the gradient at a point gives E there.
- On an E–r graph the area under the curve between two points gives the potential difference.
- Shapes — V against r follows 1/r (and −1/r for a negative charge), and E against r follows 1/r2.
Part 10 of 10Electric potential energy
- Work in a field — W = qΔV for a charge q moved through a potential difference ΔV.
- Potential energy of two charges — Ep = Q1Q2/(4πε0r), zero at infinity, with r not squared.
- It is positive for like charges and negative for unlike charges.
- Change — ΔEp = qΔV = [Qq/(4πε0)](1/r2 − 1/r1) when q moves from r1 to r2.
- Work needed — work must be done to bring like charges together or separate unlike charges, and the field does work when the opposite happens.
Last updated: