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To find the electric field at each point in vicinity of a charged particle $q$, place a small and insignificant positive charge, called test charge, $q_0$ at that point and then measure the force $\vec{F}$acting on it. The electric field $\overrightarrow{E}$ due to that point charge $q$ is defined as  \[\vec{E}=\frac{\vec{F}}{q_0}\]  Electric field is a vector quantity that its magnitude is $E=F/q_0$ and its direction is in the same direction as the force acting on the test charge. In the other words, electric field points in opposite direction of the electric force acting on a negative charged particle.   

At distance $r$ from a charged particle $q$ the magnitude of electric field is given by the following formula \[E=\frac{1}{4\pi {\epsilon }_0}\frac{\left|q\right|}{r^2}\]  Note 1: the strength of electric field around the charge $q$ is directly proportional to the magnitude of charge $q$ and inversely proportional with the square of distance $r$ from it.   Note 2: the electric field lines point away from positive charge and toward the negative charges.  

According to Coulomb's law, the magnitude of attractive or repulsive electric force between two charged particles $q_1$ and $q_2$ is proportional to the product of magnitude of charges and inversely proportional to the distance squared $r^2$ from each other and is founded by \[F=k\frac{\left|q_1q_2\right|}{r^2}\]  Or in vector form as  \[\vec{F}=k\frac{\left|q_1q_2\right|}{r^2}\hat{r}\] Where $\hat{r}$ is the unit vector along the line joining the particles to one another. In SI units, $F\to \mathrm{N}$ , $r\to \mathrm{m}$, $q\to \mathrm{C}$ and $k=9\times {10}^9\ \mathrm{N.}{\mathrm{m}}^{\mathrm{2}}\mathrm{/}{\mathrm{C}}^{\mathrm{2}}$ Note 1: the electric forces whi

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The net electric field or force of a group of point charges at each point in space is the vector sum of the electric fields due to the individual charges at that point. in the mathematical form is written as  \[{\vec{E}}_{net}={\vec{E}}_1+{\vec{E}}_2+\dots +{\vec{E}}_n\]