# A2 Physics, Electrical and Magnetic Fields, Capacitance, Electromagnetic Induction and Alternating Current, 5-8

## Electric Fields

### Coulomb’s Law

#### Static Electricity

The electrostatic effect is a result of static electricity.

• Rubbing two materials together can move electrons by friction

• Leaves a build up of charge

• Eg. A Van der Graaf generator will remove belts from the metal dome via the belt

• Approach a material of polarised molecules will cause the to realign

• Eg. Comb and paper or water

#### Charge

• Measured in coulombs

• An electron has a charge of $$-1.6\times 10^{-19}C$$

Materials can be charged by induction.

• A negatively charged object is brought close to the object

• The object is momentarily earthed

• The electrons are repelled, and flow through the earth

• This will leave a net positive charge

#### Coulomb’s Law

Coulomb’s Law states that the force between two point charges separated by a distance $$r$$ in a vacuum is directly to the product of the two charges and inversely proportionate to the square of their separation.

$$F=\frac{Qq}{4\pi\epsilon_{0}r^{2}},\nonumber \\$$

where $$\epsilon_{0}$$ is the permittivity of free space, $$8.85\times 10^{-12}Fm^{-1}$$.

• This assumes a vacuum

• Negligible difference in air

• Also assumes uniform point charges

Over microscopic distances, this force is much more important than the gravitational force, due to the small masses in comparison to charges. However, over macroscopic distances, the larger masses become more important as gravity is only attractive, whereas electrostatic forces can be attractive or repulsive.

## Electric Fields

A charged object will create an electric field around itself. Further to this, a charged particle will experience a force in this region.
Electric field lines show the force that would act on a positive test charge at that point. The proximity of the lines denotes the strength of the field. The test charge must be sufficiently small in size and charge so as not to distort the electric field.
The electric field strength, $$E$$, is the force per unit charge, in $$NC^{-1}$$.

$$E=\frac{F}{Q}\nonumber \\$$

In a radial field, field strength can be determined by using coulomb’s law. This is given by

$$E=\frac{Q}{4\pi\epsilon_{0}r^{2}}\nonumber \\$$

## Generating Electric Fields

A Van der Graaf generator can be used to generate an electric field. A Van der Graaf will normally be positively charged.

## Uniform Fields and Potential Difference

A uniform field can be demonstrated using a metallised polystyrene ball on a nylon thread between two oppositely charged plates. The uncharged ball will be attracted to the nearest plate due to its metal paint. Upon contact, the ball will be charged and repelled, and this will be repeated.
The work done, $$W$$, by an electric field in moving a particle from one plate to another (in a uniform field) is given $$W=Fd$$, with $$d$$ being the separation. Electric potential difference, $$\Delta V$$, is the work done per unit charge. Thus,

\begin{gather*} \Delta V=\frac{W}{Q} \\ \therefore Fd=Q\Delta V \\ \therefore E=\frac{\Delta V}{d} \\ \end{gather*}

As such, electric field strength can be measured in $$Vm^{-1}$$ or $$NC^{-1}$$.

## The Electron Gun

An electric field can be used to accelerate electrons.

• Electrons emitted from a heated cathode by thermionic emission

• High potential difference between cathode and anode

• Electrons accelerated towards anode

In this case

$$E=q\Delta V,\nonumber \\$$

where $$E$$ represents the energy transferred, and $$\Delta V$$ is the potential difference between the two electrodes.

## Charged Particles in an Electric Field

In a uniform field, the force is constant. Therefore, the acceleration must also be constant. This will give the charged particle a parabolic path, which can be treated using SUVAT.