# Coulomb’s Law

Coulomb’s force is the electrical force between two charges. Since there are positive and negative charges, coulomb’s force can be attractive or repulsive. However, the magnitude of the force produced by a point charge is similar to gravitational force:

\begin{aligned} F=\pm \frac{1}{4\pi \epsilon _0} \frac{Q_1Q_2}{r^2} \end{aligned}

$\epsilon_o$ is the permittivity of free space. It is a description of how well electric field lines permeates in vacuum. It has a value of $8.85\times 10^{-12} \text{m}^{-3}\text{ kg}^{-1}\text{s}^4\text{A}^2$

### Electric Field

An electric field is a region which a charge experiences an electrical force.

Similar to gravitational field strength, the electric field strength at a point is the coulomb force per unit charge placed at that point.

\begin{aligned} E=\pm \frac{1}{4\pi \epsilon _0}\frac{Q}{r^2} \end{aligned}

Properties of electric field

• Field lines are represented by arrows, starting from positive and ends at the negative.
• Field lines do not cross.
• Field lines always emerge or enters a conducting surface(s.g. metal) at a perpendicular direction.
• There are no electric field in a conductor.

The direction of the field line represents the direction of electric force acting on a positive charge when it is placed in the field. As such, the direction of electric force on a negative charge is opposite to the direction of the field lines.

### Challenge 1

Can you suggest why the electric field lines emerging or entering a conducting surface is perpendicular?

### Electric Potential

Electric potential of a point is the amount of work done in bringing a unit charge from infinity to that point.

Similar to gravitational potential,

\begin{aligned} \phi=\pm \frac{1}{4 \pi \epsilon_o}\frac{Q}{r} \end{aligned}

The electric potential energy is the amount of work done in bring a charge from infinity to that point.

The difference between electric potential and potential energy is that for electric potential, it is the energy per unit charge while in potential energy, we are considering the entire charge, which may be more than 1 coulomb.

### Relationship between electric field and potential

It is important to remember that the field strength is the negative of the potential gradient. Potential gradient means that gradient of the potential-distance graph.

### Uniform Electric Field

A uniform electric field can be produced by a pair of parallel plates. A charge placed anywhere inside a uniform field experiences the same force, regardless of whether it is nearer to the positive or negative plate.

You can think that a positive charge, if placed near the negative plate, experience more attraction by the negative plate and less repulsion by the positive plate. The same charge placed near the positive plate experiences more repulsion from the positive plate and less attraction by the negative plate. Hence the charge experiences the same force anywhere in this uniform field.