Electric potential, also known as electric potential energy per unit charge, is a fundamental concept in electrostatics that helps us understand the behavior of electric charges and their interactions. It is closely related to the electric field, and together they provide a comprehensive understanding of the electric phenomena.
Electric potential is a scalar quantity that represents the amount of electric potential energy a positive test charge would possess when placed at a specific point in an electric field. It is denoted by the symbol 'V' and measured in volts (V) in the International System of Units (SI).
When a positive test charge q is placed in an electric field, it experiences a force due to the interaction with the electric field. The electric potential at a point in space is defined as the work done by an external force in bringing the positive test charge from infinity to that point, divided by the magnitude of the test charge:
Electric Potential (V) = Electric Potential Energy (U) / Test Charge (q)
Mathematically, V = U / q
The electric potential is always a relative value, meaning it is measured with respect to a reference point, usually at an infinite distance from the source of the electric field. The reference point is conventionally assigned a potential of zero, so the electric potential at any other point will be positive or negative depending on whether the potential energy is higher or lower compared to the reference point.
The electric field (E) is a vector quantity that describes the force experienced by a positive test charge at any given point in space. It is created by one or more electric charges and extends throughout the surrounding space. The electric field is directed away from positive charges and towards negative charges.
The electric field at a point is defined as the force experienced by a positive test charge (q) placed at that point, divided by the magnitude of the test charge:
Electric Field (E) = Force on Test Charge (F) / Test Charge (q)
Mathematically, E = F / q
The electric field is also a relative value, and its direction indicates the direction a positive test charge would move when placed in the field.
Relation between Electric Potential and Electric Field:
The electric field and electric potential are related to each other in the following way:
E = -∇V
Here, ∇V represents the gradient of the electric potential. The negative sign indicates that the electric field points in the direction of the steepest decrease in electric potential.
In simpler terms, the electric field is the rate of change of electric potential in a given direction. If the electric potential is constant in a region, there is no electric field (E = 0), and conversely, if the electric potential changes significantly in a region, there will be a strong electric field.
In summary, electric potential is a measure of the electric potential energy per unit charge at a point in space, while the electric field is the force experienced by a positive test charge at that point. Understanding both concepts is crucial in analyzing and predicting the behavior of electric charges in various situations and applications.