Understanding Electric Fields Lines and how they show ‘like’ charges repelling I understand how electric field lines are suppose to be drawn, and why they are drawn from +Q to -Q and all that. What im wondering is how electric field lines explain why like charges repel? In the instance of placing a test charge q in an electric field around two +Q’s the resultant force is in line with the electric field lines. But then why, if we didnt consider a test charge but just considered our two +Q’s, the “resultant force” they would both experience does not line up with the electric field lines of the charge that is effecting it? Am I missing something fundamentally here? If so Can you help me visualize? Cheers
 A: In the pictures like yours, the density of lines is proportional to the local field strength. When two opposite charges come close you see how field lines have to squish to make way for each other (in the absence of opposite charges those lines cannot terminate and need to find their way to infinity) consequently forming regions of increased line density. Since the total energy of the field is
$$\mathcal{E} = \int dV\,  \frac{1}{2}\epsilon_0 \left|\vec{E}(\vec{r})\right|^{2},$$
this gives rise to an increase of total energy, and hence repulsion.
A: The early experimenters studying electrostatics gave electric field lines a series of properties which then enabled them to predict what might happen in a given situation.
Electric field lines,

*

*start on a positive charge and finish on a negative charge or at
infinity,

*point in the direction of the force on a positive charge,

*are in a state of tension,

*repel one another

*never cross

*are
closer together in a region where the electric field is stronger

*are at right angles to the surface of a conductor.

So in your diagrams you could say that the field lines are repelling one another and that is why the charges are repelling one another.
With opposite charge there would be field lines between the charges in a state of tension and that is why the charges attract one another.
