We know that electric charges & electric potential are related:

• An imbalance of charges creates a difference in electric potential (AKA an electric field is induced!).
• If electric charges are free to move, they will move when there is a difference in electric potential.

But what if the charges are NOT free to move?

Now we will take a look at objects which hold an IMBALANCE of charge: capacitors.

• Definition of Capacitance
  • Isolated conductors
  • Parallel-plate capacitor
• C = Q/V

---

First, consider this:
I connect a conductor to a high voltage supply WITHOUT completing the circuit. Here’s what happens:

• a potential difference is set up in the conductor
• charges will distribute themselves until the external field is opposed
• charges stop travelling once the entire conductor reaches the same potential. Now these charges are considered to be SEPARATED

How many charges are separated this way at a certain potential is given by capacitance.

---

What is capacitance?
Ratio of charge stored over potential for a conductor.

C = Q/V

Measured in farads (F)
1 farad is 1 coulomb per volt

---

Capacitance of an isolated conductor:
Any conductor can store charge if a high potential is supplied.
For simplification, here we’ll only consider spherical conductors.

From the previous chapter, we know that potential of a spherical conductor is given by:

Rearranging,

Since C = Q/V,

C = 4πε₀r

Any conductor can be a capacitor, even YOU! Try charging yourself up by rubbing an insulator, then discharging yourself on some earthed metal – you get a spark!

*Remember: insulators CANNOT have capacitance, because the charges are not free to redistribute themselves to oppose the external potential difference. Thus, the insulator cannot have the same potential everywhere, so we cannot define C.

---

What is a capacitor?
A component in an electric circuit which separates charges & stores energy which can be used at a later time.

Let’s take a look at the simplest type of capacitor: the parallel-plate capacitor.

Anatomy of a parallel-plate capacitor

As you can see, a parallel-plate capacitor consists of:

• 2 conducting metal plates
• an insulator in between
  • called a ‘dielectric’ because it can be polarised: charges cannot redistribute within it to oppose any external electric field

How does it work?

• When not connected to a battery, both plates are neutrally charged
• When the capacitor is connected to a battery, electrons travel from the plate connected to the positive terminal to the plate connected to the negative terminal
• The plates carry equal but opposite charges: each plate stores charges, but overall the capacitor does NOT store charge, just an IMBALANCE of charge
• A potential difference begins to exist between the 2 plates
• As the battery does work to separate these charges, the capacitor stores energy

https://gfycat.com/veneratedshadydinosaur

• If the external potential difference (battery) is removed, the capacitor now provides a potential difference, forcing charges to redistribute until both plates are neutral
• The capacitor discharges.

https://gfycat.com/whoppinglineariridescentshark

Capacitance of a capacitor:

C = Q/V

For parallel-plate capacitors, we take Q as the charge stored on 1 plate.

*Be careful with the word “stored” here: a parallel-plate capacitor has a net charge of 0 so it does not actually “store” any charge. BUT when we say it stores charge, we mean that 1 plate of the capacitor gains a charge of Q (while the other gains -Q).

---

Factors affecting capacitance

Area of plates, A	Larger area, more charges can be stored per unit potential So larger A, larger capacitance	C ∝ A
Distance between plates, d	Larger distance between plates, less charges can be stored per unit potential So larger d, smaller capacitance	C ∝ 1/d
Permittivity of dielectric material between plates, ε	Larger permittivity, stronger electric field allowed between plates, so more charges can be stored per unit potential So larger ε, larger capacitance	C ∝ ε

IF the dielectric is air, we can use a specific value of ε.
The permittivity of air is similar to the permittivity of free space, ε₀

Putting it all together:

C = ε₀A/d

IF the dielectric is NOT air, we can state its permittivity in reference to the permittivity of free space.
We call this value Relative Permittivity, ε_r

For a capacitor with a given relative permittivity ε_r,

C = ε_rε₀A/d