Charge must be present at a location in order for there to be electrical potential energy. Must charge also be present at a location for there to be electric potential?
I know it's no but why?
Say you have an electron at the origin.
The electron has potential energy.
The space between the electron and infinity has no potential energy if it has no charge because potential energy is charge TIMES potential.
The empty space does have potential though because there is an E field throughout that space caused by the electron.
If you put a charge into that E field, it would have potential energy and positive or negative work would have to be done to get it there depending on the sign of the charge.
Electric potential exists if work must be done to bring a "test" charge there, no matter what that test charge is. Electric potential (V) depends upon the amount and proximity of other charges.
Electric potential energy is q*V. V (the electric potential) does not depend upon qhat q is.
I find it easier to view this from a mathematical standpoint:
electric potential = electrical PE/ charge
If the charge is 0, you have
electric potential = electrical PE/ 0
you cannot have a zero in the denominator.
To understand why charge does not need to be present at a specific location for there to be electric potential, let's first define what electric potential is. Electric potential, also known as voltage, refers to the amount of electric potential energy per unit charge at a particular point in an electric field.
In simpler terms, electric potential is a measure of the potential energy that a charged object would possess if placed at that point in an electric field. It depends on the distribution of charges in the surrounding space.
Now, let's consider two scenarios:
1. Charge present at a location: In this case, the electric potential at that location would be influenced by the charges present there. The charge distribution creates an electric field, and the electric potential is determined by the interaction between the charges and the electric field.
2. No charge present at a location: Even when there is no charge present at a specific location, electric potential can still exist. This is because the electric potential at a point depends not only on the charges present at that point but also on the presence of charges in the surrounding space. The electric potential at a location can be influenced by charges located elsewhere in the electric field.
In other words, the electric potential at a point is determined by the distribution of charges in the entire electric field, not just at that specific point. The electric potential is affected by the charges' arrangement and no necessarily by their physical presence at a particular location.
Therefore, charge does not need to be present at a specific location for there to be electric potential. The electric potential at a point is a property of the electric field, which is influenced by the distribution of charges throughout the field.