Electric Potential Calculator

To understand the idea of electric potential difference, let us consider some charge distribution. This charge distribution will produce an electric field. Now, if we want to move a small charge qq between any two points in this field, some work has to be done against the Coulomb force (you can use our Coulomb's law calculator to determine this force). This work done gets stored in the charge in the form of its electric potential energy.

If we consider two arbitrary points, say A and B, then the work done (WAB​WAB​) and the change in the potential energy (ΔUΔU) when the charge (qq) moves from A to B can be written as:

• WAB​=ΔU=(VA​−VB​)qWAB​=ΔU=(VA​−VB​)q ...... (1)

where VA​VA​ and VB​VB​ are the electric potentials at A and B, respectively (we will explain what it means in the next section).

If the magnitude of qq is unity (we call a positive charge of unit magnitude as a test charge), the equation changes to:

• ΔV=(VA​−VB​)=qWAB​​ΔV=(VA​−VB​)=qWAB​​ ...... (2)

Using the above equation, we can define the electric potential difference (ΔVΔV) between the two points (B and A) as the work done to move a test charge from A to B against the electrostatic force.

Remember that the electric potential energy can't be calculated with the standard potential energy formula, E=mghE=mgh.

If we take one of the points in the previous section, say point A, at infinity and choose the potential at infinity to be zero, we can modify the electric potential difference formula (equation 2) as:

• VB​=qW∞B​​VB​=qW∞B​​

Hence, we can define the electric potential at any point as the amount of work done in moving a test charge from infinity to that point.

We can also define electric potential as the electric potential energy per unit charge, i.e.:

• V=qΔU​V=qΔU​

So you can see that electric potential and electric potential energy are not the same things.

To calculate electric potential at any point A due to a single point charge (see figure 1), we will use the formula:

where:

• qq — Electrostatic charge;
• rr — Distance between A and the point charge; and
• k=4πϵ0​1​k=4πϵ0​1​ — Coulomb's constant.

We note that when the charge qq is positive, the electric potential is positive. When the charge qq is negative electric potential is negative.

Now we will consider a case where there are four point charges, q1​q1​, q2​q2​, q3​q3​, and q4​q4​ (see figure 2). The potential at point A due to the charge q1​q1​ is:

We can write similar expressions for the potential at A due to the other charges:

To get the resultant potential at A, we will use the superposition principle, i.e., we will add the individual potentials:

For a system of nn point charges, we can write the resultant potential as:

In the next section, we will see how to calculate electric potential using a simple example.

Let us calculate the electrostatic potential at a point due to a charge of 4×10−7 C4×10−7 C located at a distance of 10 cm10 cm.

1. We are given:

   q=4×10−7 Cq=4×10−7 C and r=10 cmr=10 cm.

2. Substituting these values in the formula for electric potential due to a point charge, we get:

   V=4πϵ0​rq​V=4πϵ0​rq​

   V=0.1 m8.99×109 N⋅m2/C2×4×10−7 C​V=0.1 m8.99×109 N⋅m2/C2×4×10−7 C​

   V=3.6×104 VV=3.6×104 V

3. Hence, the electric potential at a point due to a charge of 4×10−7 C4×10−7 C located at a distance of 10 cm10 cmaway is 3.6×104 V3.6×104 V.

Now, we will see how we can solve the same problem using our electric potential calculator:

1. Using the radio button menu, choose electric potential due to a point charge.

2. Enter the value of electric charge, i.e., 4e−074e−07 and the distance between the point charge and the observation point (10 cm10 cm).

3. You can also change the value of relative permittivity.

4. The calculator will display the value of the electric potential at the observation point, i.e., 3.595×104 V3.595×104 V.

The SI unit of electric potential is the volt (V). We can say that the electric potential at a point is 1 V if 1 J of work is done in carrying a positive charge of 1 C from infinity to that point against the electrostatic force.

The unit of potential difference is also the volt. You might be more familiar with voltage instead of the term potential difference. For example, when we talk about a 3 V battery, we simply mean that the potential difference between its two terminals is 3 V.

💡 Our battery capacity calculator is a handy tool that can help you find out how much energy is stored in your battery.

To write the dimensional formula for electric potential (or electric potential difference), we will first write the equation for electric potential:

• V=qW​V=qW​

Now substituting the dimensional formula for work/energy and charge, we will get the dimensional formula for electric potential as: