Electric fields

What electric fields covers

How charge exerts a force across empty space, and how closely the mathematics matches gravity. Three lessons, the last of them explicitly a comparison, so this is the unit to take immediately after gravitational fields while the structure is fresh. It is also the prerequisite for capacitance.

The main ideas

• Coulomb's law for point charges, with charged spheres acting from their centres.
• Field strength as force per unit charge, and the radial field of a point charge.
• The uniform field between parallel plates, derived from the work done taking a charge across the gap.
• The parabolic path of a charge entering a uniform field at right angles, and why it matches a projectile's.
• Absolute potential with its zero at infinity, the work done moving a charge, and equipotential diagrams.
• Every gravitational equation paired with an electric one, and the single structural difference, that charge has two signs and so may repel.

The equations it turns on

F = Q₁Q₂4πε₀ r²$F = \frac{Q_1Q_2}{4\pi\epsilon_0 r^2}$F = Q_1Q_2/(4πε_0 r^2)

Coulomb's law for two point charges

E = FQ$E = \frac{F}{Q}$E = F/Q

the definition of electric field strength

E = Vd$E = \frac{V}{d}$E = V/d

the uniform field between parallel plates

E = Q4πε₀ r²$E = \frac{Q}{4\pi\epsilon_0 r^2}$E = Q/(4πε_0 r^2)

the radial field of a point charge

V = Q4πε₀ r$V = \frac{Q}{4\pi\epsilon_0 r}$V = Q/(4πε_0 r)

the potential near a point charge

ΔW = QΔV$\Delta W = Q\Delta V$ΔW = QΔV

work moving a charge between two potentials

Where it usually goes wrong

• There are two field strength equations for different arrangements. E = V/d is the uniform field between plates and the inverse-square form is a point charge, so the arrangement in the question decides which applies.
• Signs have to be carried. The potential near a negative charge is negative, and work done can come out negative, meaning the field does the work rather than you.
• Field lines show the direction of the force on a positive charge, not the path a charge follows. The two coincide only for a charge released from rest in a straight-line field.
• Symbols shift between this unit and capacitance: E is field strength here and stored energy there, and V is absolute potential rather than a potential difference unless a question says otherwise.

Where to start

Coulomb's law and field strength first, then electric potential. Take the comparison lesson last: if gravitational fields is already revised, it is the fastest route through this unit, because it organises both sets of equations into one table.