Chapter 5 Physics

Chapter 5.1

Charge

Charge is measured in coulombs, C. All protons have a charge of +1.6×10-19 C. Electrons have a charge of -1.6×10-19 C. The law of conservation of charge states that the total charge in any isolated system remains constant.
If we wish to make sure that there is no charge on something, we make a good contact between the object and the ground. This is called earthing.

Electric fields

An electric field is defined as a region of space in which a charge experiences an electric force.
The electric field strength is defined as the force per unit charge that would be experienced by a small positive test charge placed at that point.
The reason that a small positive test charge is used is because a larger test charge would disturb the field that is trying to be measured. Even a small test charge will have a small effect of this nature.

\begin{equation} \textup{Electric field strength = $\frac{electricforce}{charge}$}\\ E=\frac{F}{q}\nonumber \\ \end{equation}

Field strength is a vector quantity; it has a direction of force. By convention, the direction of field is chosen to be of that of the force acting on a positive charge placed in the electric field.

Combining electric fields

At any point on a straight line that passes through two point charges, the magnitude of the combined/resultant electric field may be calculated. The resultant is always directed along the line between point charges.

Coulomb’s law

Coulomb’s law can be investigated experimentally:

Two conducting spheres are charged and an electric top-pan balance is used to measure how the force changes when distance between the charges is changed. This method determines that the force and distance obey the inverse square law.
More detailed experiments show that:

\begin{equation} \text{F = constant $\times$ $\frac{q_{1}q_{2}}{r^{2}}$}.\\ F=k\frac{q_{1}q_{2}}{r^{2}}.\\ k=\frac{1}{4\pi\epsilon_{0}}Nm^{2}C^{-2}=8.99\times 10^{9}\nonumber \\ \end{equation}

Permittivity

This concept explains how \(k\) is derived. ϵ_\(0\) is the permittivity of free space.
Electric fields can pass through a vacuum, and ϵ_\(0\) is a fundemental concept represents the ability of a vacuum to transfer an electric force and field. The relative permittivity of other media is given by:

\begin{equation} \epsilon_{r}=\frac{\epsilon}{\epsilon_{0}}\nonumber \\ \end{equation}

where \(\epsilon\) represents the permittivity of the medium. The general equation for the force between two charges in a medium is:

\begin{equation} F=\frac{q_{1}q_{2}}{4\pi\epsilon_{0}\epsilon_{r}r^{2}}\nonumber \\ \end{equation}