Explain electric field and its source as well as magnetic field and its source.

Source of electric field is charge.

If $Q$ charge is static, then electric field produce around it is,

$\overrightarrow{\mathrm{E}}=\frac{k Q}{r^{2}} \cdot \hat{r} \text { or } \overrightarrow{\mathrm{E}}=\frac{Q \hat{r}}{4 \pi \epsilon_{0} r^{2}}$

where $\hat{r}$ is unit vector of position vector $\vec{r}$ and $\vec{E}$ is electric field which is vector. Force on charge particle in electric field is given by

$\overrightarrow{\mathrm{F}} =q \overrightarrow{\mathrm{E}}$

$=\frac{k \mathrm{Q} q}{r^{2}} \hat{r} \text { or } \frac{\mathrm{Q} q}{4 \pi \in_{0} r^{2}} \cdot \hat{r}$

It can convey energy and momentum and is not established instantaneously but takes finite time to propagate.

It depending on each point in space, it can also vary with time. i.e. be a function of time.

In this chapter, we will assume that the fields do not change with time.

The field at a particular point can be due to one or more charges. If there are more charges the fields add vectorially. This is called the principle of superposition.

The force on a test charge is given by $\overrightarrow{\mathrm{F}}=\overrightarrow{\mathrm{E}} q_{0}$ where $q_{0}$ is known as test charge.

Static charges produces an electric field and moving charges produce electric field and magnetic field in addition which is denoted by $\overrightarrow{\mathrm{B}}(\vec{r})$.

Magnetic field is a vector quantity and it is defined at each point in space and it depend on time.

The magnetic field of several sources is the vector addition of magnetic field of each individual source. It obey the superposition principle.