The space surrounding an electric charge has a property called ”electric field” which is drawn as a vector labeled $\overrightarrow{E}$ and represents the amount of available electric force per unit charge at any given point. Its units are equivalently $N/C$ (newtons per coulomb) or $V/m$ (volt per meter)

For simplicity, the direction of the electric field $\overrightarrow{E}$ at a given location indicates the direction in which a positive test charge $q_{test}$ would be pushed if placed at that location. A negative test charge would then be pushed in the opposite direction as shown below.

The figure above shows the electric field $\overrightarrow{E}$ created by a positive charge $q$. At various locations, we see the magnitude and direction of the electric field. The greater the magnitude, the greater the electric force ${\overrightarrow{F}}E$ acting on the test charge $q{test}$ will be. If the test charge is positive, this force acts in the direction of the electric field $\overrightarrow{E}$ (positive $q$ repels positive $q_{test}$) and if the test charge is negative, this force acts in the direction opposite the electric field $\overrightarrow{E}$ (positive $q$ attracts negative $-q_{test}$).

Thus, is the electric field at point $A$ has magnitude $E=10\ N/C$ and the test charge is equal to $q_{test}=0.2\ C$, the electric field $E$ will exert a force $F_E$ with magnitude

F_E=q_{test}E=0.2\cdot 10=2\ N

on the test charge $q_{test}$. Of course, this demonstrates that the greater the amount of charge $q_{test}$, the greater the electric force it experiences from the electric field $\overrightarrow{E}$. This makes sense because the electric field is the amount of available electric force per unit charge at any given point.

Definition: electric field lines

We will later learn how to predict the direction of the electric field created by a given charge distribution but for now we consider the following two (separate) cases of a positive point charge $q$ and a negative point charge $-q$ and we draw the electric field lines that surround them.

While it is convenient to see the magnitude and direction of the individual electric field vectors in the figure above, it makes representing electric fields tedious in practice as it requires drawing the vector plots every time. Thus, we introduce electric field lines which are smooth curves that connect all the individual vectors as shown below.

This unfortunately removes information about the magnitude of the electric field at any given point but makes representing electric fields much easier and convenient. We therefore generalize this representation to any electric field surrounding a charge and introduce the following properties of electric field lines.

Properties of electric field lines:

1. The electric field $\overrightarrow{E}$ at any point is tangent to the electric field line and points in the direction of the field line.

2. The electric field lines of a given charge distribution cannot intersect.

3. The electric field lines either:

3.a. originate at a positive charge and extend to infinity

3.b. originate at infinity and end at a negative charge

3.c. originate at a positive charge and end at a negative charge if both charges are present in the same region

4. In a region without any charge, the closer the electric field lines, the stronger the electric field.

5. If there is more than one charge, the number of field lines attached to the charge is directly proportional to the amount of charge.

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