§ 18.1 Electric fields and field lines
Key ideas
- Electric field strength is the force per unit positive charge, E = F/q; the force on a charge is F = qE.
- Field lines point in the direction of the force on a positive charge: away from positive, towards negative charges.
Equations
E = F / qfield strength = force per unit positive chargeN C⁻¹
Fig. 1 · Radial fields: the lines leave a positive charge and enter a negative one, always pointing the way a small positive test charge would be pushed.
Watch out: field lines show the force on a positive charge. A negative charge feels a force in the opposite direction to the field line through its position.
§ 18.2 Uniform electric fields
Key ideas
- Between parallel plates the field is uniform: evenly spaced parallel lines, with E = ΔV/Δd.
- A charge moving through the field follows a parabolic path, just like a projectile under gravity.
Equations
E = ΔV / Δduniform field between parallel platesV m⁻¹
Fig. 2 · A uniform field deflects a moving charge along a parabola: constant velocity along the plates, constant acceleration across them, exactly like projectile motion.
Watch out: the field between parallel plates is uniform, so E does not depend on position between them. The force on a charge is the same near either plate, unlike the 1/r² field of a point charge.
§ 18.3 Electric force between point charges
Key ideas
- A charged sphere behaves as a point charge at its centre.
- Coulomb's law is an inverse-square law: like charges repel, unlike attract.
Equations
F = Q₁Q₂ / (4πε₀r²)ε₀ = 8.85 × 10⁻¹² F m⁻¹N
Watch out: gravity is always attractive, but the electric force can attract or repel. Carry the signs of the charges through, or state the direction (towards or away) explicitly.
§ 18.4 Electric field of a point charge
Key ideas
- The field of a point charge is radial and obeys an inverse-square law, mirroring g = GM/r² for gravity.
Equations
E = Q / (4πε₀r²)radial field of a point chargeN C⁻¹
Watch out: field E falls as 1/r² but potential V falls as 1/r. Doubling the distance quarters the field strength yet only halves the potential; do not use the same power for both.
§ 18.5 Electric potential
Key ideas
- Electric potential is the work done per unit positive charge in bringing it from infinity to the point.
- The field is the negative gradient of the potential, E = −dV/dr.
- Near a positive charge V is positive (work done against repulsion); near a negative charge V is negative.
Equations
V = Q / (4πε₀r)potential of a point charge, zero at infinityV
Ep = Qq / (4πε₀r)potential energy of two point chargesJ
Watch out: unlike gravitational potential, which is always negative, electric potential can be positive or negative depending on the sign of the charge that sets up the field. Keep the sign of Q.