EM-10 · Electrostatics field

Dielectrics and Polarization

Put a dielectric in a field and its molecules polarize, weakening the net field. Raise the relative permittivity ε_r to see the dipoles split apart and the field weaken by a factor ε_r.

Raise ε_r and watch the field weaken

A dielectric slab sits in a uniform external field. Raise the relative permittivity ε_r. How far do the dipoles inside split apart? What happens to the net field (the gold arrow)?

Relative permittivity ε_rε_r = 3.0

Drag to orbit. The slider sets the relative permittivity ε_r.

The net field inside the dielectric

E = E₀/ε_r · the net field weakens by a factor ε_r

P = ε₀(ε_r − 1)E · molecular dipoles line up

Net field (vs external) · 33%

Middle

What a dielectric is

A dielectric is an insulator with almost no free electrons. Unlike a conductor, charge cannot flow freely. Yet under a field, the positive and negative charges inside each molecule shift slightly in opposite directions, forming dipoles. Charge does not flow, but separates a little in place. This is called polarization.

Polarization, dipoles align

Apply an external field E₀ and countless molecular dipoles line up with it. The degree of alignment, as dipole moment per unit volume, is the polarization P. Inside the bulk neighbouring + and − touch and cancel, but at the two end surfaces uncancelled bound charge appears — a layer of − on one face and + on the other.

ObserveE = E₀/ε_r

Inside a dielectric the net field is ε_r times weaker.

The net field weakens

The surface bound charge creates a field inside the dielectric opposite to the external one. Running from the + surface to the − surface, it cancels part of E₀. So the net field inside is weaker than outside. The factor by which it weakens is the relative permittivity ε_r: E = E₀/ε_r. Air has ε_r near 1; water about 80, weakening the field greatly.

ChooseP = ε₀(?)E

Polarization is ε₀ times (ε_r − 1) times the field.

D and permittivity

To handle polarization separately, we define the electric displacement D = ε₀E + P. In a linear dielectric P is proportional to E, so D = εE cleanly, with permittivity ε = ε_r ε₀. The virtue of D is that it ignores bound charge and responds only to free charge. So Gauss’s law in terms of D reads ∮D·dA = Q_free: even with a dielectric present, you count only the free charge.

Fill inε = ?

Permittivity is relative permittivity times the vacuum value.

On your ownD = ? = εE

Displacement is the vacuum term plus polarization, equal to εE.

Back to the first screen

On the first screen, raising ε_r split the dipoles inside the dielectric more widely and deepened the surface bound charge. The opposing field they create ate into the external field, and the gold arrow for the net field grew shorter and shorter. The factor of weakening is ε_r itself: E = E₀/ε_r. A dielectric tames the field through polarization alone, without ever letting charge flow.

Put a dielectric in a field and its molecules polarize, separating positive and negative charge slightly. The bound charge on its surfaces makes a field opposing the external one, so the net field weakens by a factor ε_r: E = E₀/ε_r. The polarization is P = ε₀(ε_r − 1)E, the permittivity ε = ε_r ε₀, and the displacement D = ε₀E + P = εE.

What comes next

Dielectrics pair naturally with capacitors. Fill the gap between two plates with a dielectric and, for the same voltage, the weakened field lets the plates hold ε_r times more charge — so the capacitance grows by ε_r. The next unit (EM-11) treats capacitance C = εA/d and counts this effect exactly.