Yes, electric potential can be negative, and understanding why requires a clear grasp of what this quantity represents. Electric potential, often called voltage, is defined as the electric potential energy per unit of electric charge. It is a characteristic of the electric field itself, not the charge placed within it. This scalar quantity is measured in units of joules per coulomb, or volts (V). The sign of the electric potential depends directly on the arbitrary choice of a zero reference point.
What Electric Potential Represents
Electric potential (\(V\)) is fundamentally defined by the work required to move a positive test charge within an electric field. Specifically, it is the amount of work done by an external force to slowly move a unit positive charge from a defined reference point to the point in question. The relationship between electric potential and electric potential energy (\(U\)) is \(V = U/q\), where \(q\) is the test charge.
The conservative nature of the electrostatic force means the work done is independent of the path taken, depending only on the starting and ending positions. This mathematical property allows physicists to define a scalar potential function that simplifies calculations compared to dealing with the vector electric field. Since the test charge is divided out, the resulting potential value is a property of the source charges creating the field.
A high positive electric potential indicates that significant work must be done against the electric field to bring a positive charge to that point. Conversely, a low potential means less work is required, or that the field would naturally push the positive charge toward that location. The concept is rooted in potential energy, which measures the capacity to do work based on position.
The Importance of the Zero Reference Point
Negative electric potential exists because electric potential is a relative quantity, not an absolute one. Only the difference in potential between two points, known as voltage, has physical significance. To assign a single value to a point, a reference location must be chosen and defined as having zero potential (\(V=0\)).
Two standard conventions are used for setting this zero reference point. In circuit analysis and practical applications, the common reference is often called “ground,” typically a connection to the Earth or a specific point in a circuit. Any point at a lower potential than this chosen ground reference will be assigned a negative voltage.
In theoretical physics, especially when dealing with isolated charges, the zero potential is conventionally set at a point infinitely far away from the source charges. This choice is convenient because the electric field strength decreases with distance, effectively becoming zero at infinity. If a point has a negative potential under this convention, it means the potential at that location is lower than the potential at infinity.
The situation is analogous to measuring elevation, where sea level is designated as zero feet. A mountain peak has a positive elevation, while a point below sea level has a negative elevation. The negative sign indicates that the location is simply “lower” in potential than the arbitrary zero reference.
Interpreting Negative Electric Potential
When the standard convention of setting \(V=0\) at infinity is used, a negative electric potential at a point has a clear physical meaning related to attraction and repulsion. A negative potential is created by a net negative source charge. For example, the region around an isolated electron will have a negative electric potential.
If a positive test charge were placed in this negative potential region, the electric field would naturally pull it towards the negative source charge. This indicates the positive test charge is in a state of lower potential energy than if it were at the zero reference point (infinity). The electric field does positive work on the charge as it moves toward the source.
To move the positive test charge away from the negative source charge and back toward the zero reference point at infinity, an external force must do positive work. The negative potential sign signifies that the field is attractive to a positive test charge. This represents an “energy deficit” that must be overcome to separate the charges.