Electric Fields

The plastic ball dangles on a string. In the electric field with a potential difference (p.d.) of 20 kV it accelerates very strong and you can observe amazing lightning. But why do we have this forces on a plastic ball?

The answer: The force is a result of different charges.

Coulomb wanted to know it more presicely. He observed that force can be attractive or repulsive. Since there are two different types of charge - positive and negative - he found out: different charges attract each other, identical charges repel.

Coulomb observed two charges by experiment and identified that the force is

• directly proportional to each charge $Q_1$ and $Q_2$,
• inversly proportional to the square of their distance $r$.

$$F=\frac{k\cdot Q_1 Q_2}{r^2}$$

The value for the constant of proportionality $k$ is $9.0 \cdot 10^9~Nm^2/(As)$. In vacuum or air it is written to $k=\frac{1}{4\pi \epsilon_0}$, where $\epsilon_0=8.85 \cdot 10^{-12}As/(Vm)$ is the permittivity of free space. Any other insulating material has a permittivity $\epsilon$ greater than $\epsilon_0$.

During thunderstorm we observe lightning. We say there is an elctric field around the lightning. It is possible to see the shape of an electric field with castor oil and semolina grain as shown and a p.d. of 20 kV. Field lines always enter the surface vertically, have a direction and as stronger the field the more dense the lines.

We introduce the electric field strength $E$ which just tells us the voltage drop per meter distance or the force excerted on a charge.

$$E=\frac{V}{d}=\frac{F}{Q}~~~~[E]=\frac{V}{m}=\frac{N}{As}$$

During thunderstorm we have $E=200,000~V/m$. This means at an altitude of 1000 m an electric potential of $200,000,000~V$.

To ionize air we need $E = 3,000,000~V/m$. If the humidity increases this value decreases. Further more if the distance between clouds and earth decreases the electric field strength increases. So the air will ionize and for 10 ms a very high current of around $10,000~A$ will flow.

So we can estimate the energy of lightning:

$$E_{\text{el}}=V \cdot I \cdot t=5500~kWh$$

A car in an electric field is a save place.

Try the following experiment: You enter a square of 2x2 m and assume you are an electron. The next person (also negative) enters the square. Just try to behave like two identical charges. The third person will enter the square. Where is the positioning of everybody? Not sure, yet? Try a fourth and fifth person.

If a lightning hits the car the electrons will flow through the metal cage of the car. Since electrons repel each other they stay at the outside of the car. As long as you are inside the car and you do not touch the outside, nothing will happen.

Fast moving beams of electrons can be generated by an electron gun. Thermionic emission is generated by a heated cathode where electrons can escape. The electrons are accelerated by the positive anode. As the electrons are accelerated they loose potential energy, but win kinetic energy.

$$1/2mv^2=eV$$

Some elctrons pass through the anode and can be deflected by another electric field.

$$F=eE=e\frac{V}{d}$$