Electric Potential Calculator

Created by Luciano Mino
Last updated: Aug 24, 2022

Our electric potential calculator can obtain the electric potential at any distance from a single point charge or a number of point charges (up to ten).

If you don't know what the electric potential is, don't worry. Within this short article, we will cover:

  • Electric potential definition;
  • Electric potential formula/equation;
  • Electric potential due to a point charge; and
  • Electric potential due to a system of point charges.

Let's start!

What is the electric potential? Electric potential formula

We define the electric potential of a point charge at a point in space as the work required to bring a 1 C1\ \text{C} charge from infinity to that location.

Sounds confusing? Let's do some math first so you can start working with the electric potential calculator.

💡 Alternatively, check our electric field calculator to get a proper introduction to this topic.

Assume we had two positive point charges, qq and QQ, separated by a distance of rr.

If you remember, Coulomb's law describes the force FF between these particles:

F=keqQr2F = \frac{k_{e}qQ}{r^{2}}

where kek_{e} is Coulomb's constant.

Now, assume we tried to bring the charges closer by moving qq from r1r_{1} to r2r_{2} (r1>r2r_{1} > r_{2}). For that, we would need to do work against this repulsive force:

dW=keqQr2drdW = -\frac{k_{e}qQ}{r^{2}}dr

by integrating between r1r_{1} and r2r_{2} we get:

Wr1r2=keqQ(1r21r1)W_{r_{1}r_{2}}=k_{e}qQ(\frac{1}{r_{2}}-\frac{1}{r_{1}})

Lastly, if we replace one of the charges with a unit test charge (a 1 C1\ \text{C} positive charge) and set our initial point at infinity, we obtain the electric potential equation for a point charge:

V(r)=keQrV(r) =\frac{k_{e}Q}{r}

This potential depends only on rr and QQ, and its unit is the volt (V).

🔎 Electromagnetism is an interesting topic with some counterintuitive repercussions, such as the force between current-carrying wires. Read more about it in this calculator!

Electric potential due to a system of point charges

We can extend this definition to a system of multiple point charges easily.

The electric potential of multiple point charges qiq_{i} at a point in space is simply the vector sum of each individual electric potential:

V(r)=keiqirriV(r) = k_{e} \sum_{i}\frac{q_{i}}{|r-r_{i}|}

With our electric potential calculator, you can input up to ten point charges and it will output the resulting electric potential at any point. Give it a try!

🙋 Our electric potential calculator is straightforward: input the charge and the distance, and it will automatically output the electric potential at that position.

Luciano Mino
I want to calculate.....
Electric potential
due to a point charge
Electric potential due to a point charge.
Charge (q)
C
Distance (r)
μm
Electric potential (V)
x10⁶
V
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