Introduction

When we think of an electric field, we imagine a force pulling on a charge. But what if the charge is at rest? How can you measure the electric field around such a charge? The answer is that you need to build up an electrostatic potential by adding together contributions from individual charges. This means that there must be some way for adding up these contributions such that each one has its own unique sign and magnitude—otherwise, it would be impossible to tell whether the field was positive or negative! In this post, I’ll show how electrostatic potentials arise from point charges and why they’re so important for understanding fields.

The electrostatic field around a point charge is not constant.

As you move away from a point charge, the electrostatic field decreases. The electrostatic field is zero at infinity (that is, if you took an infinitely long wire and stretched it out indefinitely). It’s also positive inside the charge and negative outside of it.

Potential energy increases as you move closer to the charge.

We have been talking about potential energy and electric fields, but what exactly is potential energy? It’s the amount of work that would be required to move an object from one point in space to another point in space. For example, if you have a ball sitting on top of a hill and then roll it down into a valley below, your body will exert effort (i.e., do work) on that ball in order to get it moving from one location to another. In this case, we can say that there was some amount of stored energy within our system because there was an imbalance between how high up our starting point was compared with where we wanted our final destination location being located at–and if nothing else were done besides letting gravity do its thing then those two points wouldn’t be connected by anything other than air molecules bumping into each other over time (which isn’t really enough).

Point charges have regions of positive and negative potential.

You can think of an electric field as a set of arrows that point in the direction that an object would be pushed if it were placed in that field. For example, if you put your finger on top of a positive charge, your finger would be pushed away from the charge because there are more positive charges around it than negative charges (which attract).

If you place two point charges at different locations with respect to each other and draw their respective electric field lines:

The gradient of the electrostatic potential is related to the force on a test charge.

The gradient of the electrostatic potential is related to the force on a test charge. The force on a test charge is proportional to its electric potential energy, or the work done by its field in moving it from one point in space to another. This relationship can be expressed as

$$F = \frac{V}{d}$$ where F is your force, V is your potential difference (voltage), and d is distance traveled by your object. The term “voltage” here refers not only to literal voltages but also any kind of difference in electric potential between two points in space (which need not have any actual voltage).

The general equation for calculating an electric field at any given point in space looks like this: $$E = -\frac{k}{r^2}\int_{0}^{r}(e_1 \cdot r) dr$$ Where k is Coulomb’s constant (8*PI*10^9 Nm^2/C2) and r represents distance from some origin point within which we wish calculate our total electric field strength

Takeaway:

So, we’ve seen that the electrostatic potential increases as you get closer to a charge. The question now is how do we use this information?

Well, it turns out that if we know the electrostatic potential at any point in space and know what charges are present in that region of space (or could be placed there), then we can calculate their force on each other. That’s really all there is too it!

The electrostatic potential is a useful way to visualize the electrostatic field around a point charge. It can help you understand how the field changes as you move closer or farther from the charge, and it’s also important for calculating things like forces on test charges.