Electric potential is a fundamental concept in physics. When we have a charge Q, it creates an electric field in the space around it. This field represents the charge's ability to exert forces on other charges. The electric potential V equals k Q over r, where r is the distance from the charge. But why does this potential exist at all?
The answer lies in the electric field. A source charge Q creates an electric field E in the space around it. This field has magnitude E equals k Q over r squared, and points radially outward from positive charges. The field represents the force per unit charge that would be exerted on any test charge placed at that location. When we place a test charge q in this field, it experiences a force F equals q times E.
To understand why potential exists, we need to consider work and energy. When we move a test charge in an electric field, we must do work against the electric force. This work gets stored as electric potential energy. The work done equals the integral of force dot dr along the path. This stored energy represents the potential energy U equals q times V that the charge has at that position due to the source charge's field.
Electric potential V is defined as the potential energy per unit charge. V equals U over q. This means that potential represents the energy that a unit positive charge would have at that location. The key insight is that potential exists at every point in space around the source charge, even when no test charge is present. The formula V equals k Q over r gives us the potential at any distance r from the charge Q. These equipotential surfaces show points of equal potential.
In summary, a charge creates electric potential because it fundamentally modifies the space around it. The source charge establishes an electric field that extends throughout space. This field represents the ability to do work on other charges. When work is done, potential energy is created. Electric potential is simply the potential energy per unit charge, creating an energy landscape in space. The formula V equals k Q over r quantifies this potential at any distance. Importantly, this potential exists everywhere around the charge, even when no test charges are present. It's an intrinsic property of the space modified by the source charge.