5. Electrostatic effects
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Parallel plate capacitor P.23
A capacitor is something that stores charge (more precisely, it stores a separation of charge). The amount of charge it stores is proportional to the voltage and the constant of proportionality is the capacitance:

Q=C.V

Charging and discharging a capacitor
Picture 5.6 A simple parallel plate capacitor will store a separation of charge. When it is connected to a lamp, the charge will flow off the capacitor and light the lamp temporarily.
A simple capacitor
We can build a simple, effective capacitor with two parallel plates. The plates are separated by an insulator – possibly air. In picture 5.6, the top plate will become positively charged and the bottom plate will be negatively charged. These opposite charges will help to hold each other onto the plates. However, the amount of charge is still limited by the voltage and the dimensions of the capacitor.
What affects the capacitance?
The capacitance of a parallel plate capacitor depends on:
  • the area of the plates
  • the separation of the plates
  • the filling between the plates.
Capacitors in parallel
Picture 5.7 Adding two similar capacitors in parallel is like doubling the area of one of the sets of plates.
Area
Look at picture 5.7. It shows two similar sets of plates. They each have the same capacitance and hold a charge of 4 mC. The total charge is therefore 8 mC (twice the charge on one set of plates). We could make the same capacitor by simply joining the sets of plates together – i.e. doubling the area of the plates. In which case, by doubling the area, we have doubled the charge. So the capacitance is proportional to the area.

        C µ A

Changing separation
Picture 5.8. Illustrating separation
Separation
In picture 5.8, the positive charges on the top plate are all repelling each other. That’s why it gets more difficult to add extra charge. However, the negative charges on the bottom plate will tend to reduce this repulsive effect. The closer the two plates are, the bigger the attractive force of the opposite plates and the more charge we can get onto the plates at a given voltage, i.e. the capacitance goes up as the separation, d, goes down. We can show that:

        C µ 1/d

The filling
The plates are separated by an insulator – often air. However, some insulators behave as a dielectric. This means that their molecules can have an electrical dipole. The molecules will then line up in the electric field between the plates. Let's say the top plate is positive. So the top of the dielectric will become negative (and the bottom positive). Again, this will reduce the repulsive effect of all the positive charges on the top plate and therefore allow more charge onto the plate (at a given voltage). We measure the effect of the dielectric with a constant called the permittivity (with the symbol e). A bigger permittivity will allow more charge onto the plates so the capacitance is proportional to the permittivity of the insulator between its plates:

        C µ e

Putting it all together
We can combine the three proportional statements into one equation:

        C = Ae/d

This tells us the capacitance of a parallel plate capacitor.

Conveyer capacitance
The production line in an aerosol filling plant is built around a rubber conveyer belt. This belt is constantly moving and therefore rubbing against its mountings. It is like one long parallel plate capacitor that is being charged by rubbing. So what if the charge built up too much? There might be a spark. To avoid this, we have to make sure that the belt ‘capacitor’ is discharged more quickly than it can charge up. We’ll see how in the next section.
commercial capacitors photo
Picture 5.9 Some commercial capacitors.
Question 18
Picture 5.6 shows a parallel plate capacitor. The plates are 20 cm square and are 3 mm apart. They are separated by air, whose permittivity is approximately that of free space: 8.85 x 10-12 F m-1.
a) What is the capacitance of this capacitor?

b) How much charge will it hold at a voltage of 10 V?

c) Commercial capacitors are often made from a spiral of two conductors wound up inside a tube (picture 5.9). Explain how this increases the capacitance.

Click shift/return to get a line break in your answer

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Summary                                           Close
  • a pair of parallel plates makes a simple capacitor
  • the capacitance is proportional to the area
  • it is inversely proportional to separation
  • the capacitance depends on the material between the plates
  • C = Ae/d