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 qqq 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 (WABW_{AB}WAB​) and the change in the potential energy (ΔU\Delta UΔU) when the charge (qqq) moves from A to B can be written as:

• WAB=ΔU=(VA−VB)qW_{AB} = \Delta U = (V_A – V_B)q

  W

  A

  B

  ​

  =

  Δ

  U

  =

  (

  V

  A

  ​

  −

  V

  B

  ​

  )

  q

  …… (1)

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

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

• ΔV=(VA−VB)=WABq \Delta V = (V_A – V_B) = \frac{W_{AB}}{q}

  Δ

  V

  =

  (

  V

  A

  ​

  −

  V

  B

  ​

  )

  =

  q

  W

  A

  B

  ​

  ​

  …… (2)

Using the above equation, we can define the electric potential difference (ΔV\Delta VΔV) 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=mghE=mgh.