Electric Potential — Definition
Definition
Imagine you have a tiny, imaginary positive charge, let's call it a 'test charge', that you want to move around in space. Now, if there are other charges already present, they will create an 'electric field' around them. This electric field exerts forces on our test charge. To move this test charge against the electric force (or sometimes with it), you, as an external agent, have to do some 'work'.
Electric potential at a specific point in space is essentially a measure of how much work you would need to do to bring that tiny unit positive test charge from a very, very far away place (what we call 'infinity', where the electric field from the other charges is considered negligible) all the way to that specific point.
Crucially, we assume you do this slowly, without accelerating the test charge, so that its kinetic energy doesn't change. This ensures that the work done is solely converted into potential energy.
Think of it like lifting an object against gravity. The higher you lift it, the more gravitational potential energy it gains. Similarly, moving a positive test charge to a point of higher electric potential means you've done positive work against the electric field, and the charge has gained electric potential energy. If you move it to a point of lower potential, the electric field would do positive work, and the charge would lose potential energy.
Electric potential is a scalar quantity, meaning it only has magnitude, not direction. This makes it much easier to work with compared to the electric field, which is a vector. The unit for electric potential is the Volt (V), named after Alessandro Volta.
One Volt is defined as one Joule of work done per Coulomb of charge (). So, if a point has an electric potential of 10 Volts, it means that 10 Joules of work are required to bring a 1 Coulomb positive test charge from infinity to that point.