Meaning of the Equation

The electrostatic potential difference due to a charge Q between two positions A and B is defined as the amount of work done in bringing a unit point charge from point A to B without acceleration.

We first encountered this equation when we were in school , remember ? However, as simple as it seems understanding this equation becomes a difficult task for most school students. Let us try to figure out the exact meaning of this equation. The potential due to a charge Q at a point is defined as the amount of work done to bring a unit positive charge from infinity to that point without acceleration. Further, the potential difference between two positions A and B is defined as the amount of work done per unit charge to move the charge from point A to B.

Another way to understand this is by taking the analogy of potential energy. We all know by the famous work-energy theorem that work can be interchanged into energy and vice-versa. So, we may define potential difference between two points in the electric field of a charge Q as the potential energy gained or lost by a unit charge in moving from positions A to B. Having difficulty in imagining the real picture? Well, I understood these concepts by the following examples :

Case-I:

Assume that you are enjoying Bone fire picnic with your friends. There is a natural gradient of heat around the fire as in the places closer to the fire will have higher temperatures, whereas far away from the bonfire, it is way cooler. Suppose that you are feeling cold while sitting at a position A (say) away from the bonfire, so you get up from A and sit at a relatively warmer place which is closer to the bonfire, let’s say position B. Now, you can feel an increase in the amount of warmth at position B as compared to position A. Well, this is exactly the difference in heat potentials between the two positions A and B and this is how the electrostatic potential difference is except that it is related to the electric field of a charged particle rather than the heat of a bonfire.

Case-II

Now, consider the case when your class teacher is little bothered about your safety while sitting at a position B nearer to the bonfire and she suggests you to go back to your position A. When you move from the warmer position B to position A, you again feel a change in temperature between the two positions. However, the change this time is towards the cooler temperature. The amount of change in both cases is same, however, as you move away from the source of heat, the amount of warmth is reduced and vice-versa. So, the increase difference in heat at the two places is just like the potential energy gained by a charge as it moves from point A to B in the electric field of a charge

The S. I. unit of potential is Volt and 1 Volt signifies 1 Joule per Coulomb. Now, Let us talk about the potential difference delivered of a battery. If you might have paid attention to the everyday cells we use in our wall clocks, you might have noticed that a -1.5 V is indicated on one and +1.5 V is indicated on another end of the battery leading to a potential difference of 3V. What does this mean?

Now, we know that current flows in a circuit by the movement of charged particles. This means that a unit charged particle when moves from one end of the battery to another, it gains an energy of 3 Joules and when it moves inside the circuit, it loses this 3 Joules of energy.