Summary — What This Chapter Covers
- E = F/q (force per unit positive charge), so F = qE; field lines run from + to −.
- Uniform field between parallel plates: E = ΔV/Δd. A charged particle there has constant acceleration and follows a parabola.
- Coulomb's law: F = Q1Q2/(4πε0r2); a charged sphere acts as a point charge at its centre.
- Point charge: E = Q/(4πε0r2), V = Q/(4πε0r), EP = Qq/(4πε0r).
- Field strength = − potential gradient: E = −dV/dr.
1. Electric Fields and Field Lines
18.1
Force per unit positive charge
An electric field is a region in which a charge experiences a force: another example of a field of force. The electric field strength at a point is the force per unit positive charge on a small test charge placed there. Its unit is N C−1, equivalent to V m−1.
Field lines show the direction of the force on a positive charge: they start on positive charges and end on negative charges, never cross, and are closer together where the field is stronger. Around a point charge they are radial; between parallel plates they are parallel and equally spaced.
Definition
E = F/q F = qE
Worked Example
Find the force on an electron in a field of strength 5.0 × 103 N C−1.
2. Uniform Electric Fields
18.2
Parallel plates
Between two parallel plates with p.d. ΔV and separation Δd, the field is uniform (except near the edges) with strength E = ΔV/Δd. A charged particle there feels a constant force qE, so it has constant acceleration qE/m parallel to the field.
A particle entering at right angles to the field behaves like a projectile: its velocity component perpendicular to the field is unchanged, while it accelerates uniformly along the field. The path is a parabola. A particle moving along the field lines simply speeds up or slows down.
Uniform field
E = ΔV/Δd a = qE/m
Worked Example
Plates 4.0 cm apart and 5.0 cm long have a p.d. of 1000 V. An electron enters midway between them at 2.0 × 107 m s−1, parallel to the plates. Find its deflection as it leaves.
3. Electric Force Between Point Charges
18.3
Coulomb's law
Two point charges exert equal and opposite forces on each other, proportional to the product of the charges and inversely proportional to the square of the separation. Like charges repel, unlike attract. For a point outside a charged spherical conductor, the charge acts as if concentrated at the centre. ε0 is the permittivity of free space, 8.85 × 10−12 F m−1, and 1/(4πε0) = 8.99 × 109 m F−1.
Coulomb's law
F = Q1Q2/(4πε0r2)
Worked Example
Find the force between charges of +3.0 nC and −5.0 nC placed 0.10 m apart.
Practice Question
In a hydrogen atom the electron and proton are 5.3 × 10−11 m apart. Compare the electric and gravitational forces between them.
4. Electric Field of a Point Charge
18.4
E = Q/(4πε₀r²)
neutral point
Point charge
E = Q/(4πε0r2)
Memorise