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# Introduction to electric fields

## Electric fields and forces

An electric field is a region of space in which an electric charge experiences a force.

Electric fields are caused by electrical charges.

An electron is surrounded by an electrical field.

A uranium ion containing 92 protons and 91 electrons is surrounded by an electric field.

An electric field is an example of a force field or field of force.

A field of force is a region in space in which an object experiences a force. The magnitude and direction of the force on the object depends on its position.

The attractive force on a proton increases if it gets closer to an electron.

Gravitational fields are also fields of force.

The electric field of the charged disc causes the paper strips to be attracted to it.

## Electric field lines

Electric fields are visualised by drawing electric field lines.

An electric field line always points in the direction a positive charge would accelerate if it were placed into the field.

Positive charges are always attracted to negative charges. For this reason, electric field lines always point from positive to negative.

Electric field lines are closer together where the electric field is stronger.

This is similar to the use of contour lines on a map to indicate height.

In the diagram below, the electric field is stronger on the left than on the right as the field lines are closer together.

Electric field lines point from positive to negative.

## Fields of a single isolated point charge

A point charge is a charge with no physical dimensions. This means that a point charge only occupies a single point in space.

An isolated charge means that we are only considering one charge.

Electric field pattern generated by two isolated point charges. Positive (left) and negative (right).

The electric field lines of an isolated point charge are radial and do not intersect. They extend outwards from the charge in all directions (or extend inwards to the charge from all directions.)

The distance between the field lines increases as you go further from the charge. This means the field gets weaker as you get further away.

The field lines extend outwards to infinity. This means that there is still an electric field even at very large distances from the charge!

However, the field becomes so weak at large distances that its effects can be ignored.

## Fields of two point charges

The electric fields of two point charges add up to give the resultant electric field.

The electric field generated by two point charges placed close to each other.

In the case of two positive charges, the field lines all point outwards.

The electric field pattern generated by two negative charges is the same as that produced by two positive charges, except that the field lines all point inwards.

In the case of two unlike charges, the electric field lines point from the positive charge towards the negative charge.

As you get very close to each individual charge, the electric field looks exactly the same as for an isolated charge.

## Coulomb's law

Coulomb's law states that the magnitude of force between two charges is directly proportional to each of the charges and inversely proportional to the square of the distance between them (i.e. $F\propto Qq/r^{2}$).

This proportionality relation is very similar to the universal law of gravitation, except that charge is replaced by mass.

Note that charges can be either positive or negative while mass is only positive. Therefore, an electric force can be either attractive or repulsive.

The formula for Coulomb's law is:$$F=\frac{Qq}{4\pi\epsilon_{0}r^{2}}$$$F$ is the magnitude of the force, $Q$ and $q$ are the charges and $r$ is the distance between the two charges.

$\epsilon_{0}$ (pronounced as "epsilon naught") is a constant called the permittivity of free space and has a value of $8.85\times10^{-12}\text{F m}^{-1}$ (farads per metre). This constant is frequently used in electromagnetic calculations.

Positive values for the force indicate that the force is repulsive while negative values indicate that the force is attractive.