What is the difference between voltage and electric potential?

Electric Potential:

Electric potential, also known as electric potential energy per unit charge, is a scalar quantity that represents the potential energy a positive test charge would have at a specific point in an electric field. It is a measure of how much work would be done on a positive test charge to move it from a reference point (often taken at infinity) to the given point in the electric field, divided by the charge of the test particle.

In mathematical terms, electric potential (V) at a point in an electric field is given by:

V = U / q

Where:

V = Electric potential at the point

U = Electric potential energy of the test charge at that point

q = Magnitude of the test charge

Electric potential is measured in volts (V) or joules per coulomb (J/C).

Voltage:

Voltage, also known as electric potential difference or electrical potential drop, is a measure of the difference in electric potential between two points in an electric circuit. It quantifies the work done by an electric field in moving a charge between two points.

In simpler terms, voltage is the driving force that pushes electric charges through a conductor (such as a wire) in an electric circuit. When there is a voltage across a circuit, it causes charges to move from higher potential (positive) to lower potential (negative) points.

Mathematically, voltage (V) between two points A and B is given by:

V = ΔV = V_B - V_A

Where:

V = Voltage between points A and B

V_A = Electric potential at point A

V_B = Electric potential at point B

Voltage is also measured in volts (V) or joules per coulomb (J/C).

In summary, electric potential is the potential energy per unit charge at a specific point in an electric field, while voltage is the difference in electric potential between two points in an electric circuit. Both are measured in volts, but electric potential is used in the context of electric fields and charges at a single point, while voltage is used in circuits to describe potential differences between two points.