The electric field, often symbolized as the E-field, is the invisible influence that surrounds any object possessing an electric charge. This field is a fundamental concept in physics, describing how charged particles exert forces on one another without physical contact. The electric field is classified as a vector quantity, meaning it has both a specific strength and a direction in space. The standard international system (SI) provides two common units for this measurement, each derived from a different perspective on the field’s action.
The Primary Unit: Force per Charge (Newtons per Coulomb)
The most direct way to define and measure the electric field is by considering the force it exerts on a charged object. The foundational definition of the electric field strength (\(E\)) is the force (\(F\)) experienced by a small positive test charge (\(q\)) placed at that point, expressed mathematically as \(E = F/q\). Because of this definition, the primary unit for the electric field is derived from the units of force and charge.
The unit of force in the SI system is the Newton (N), and the unit of electric charge is the Coulomb (C). Combining these yields the Newton per Coulomb (N/C). An electric field measured in N/C directly tells you the amount of force, in Newtons, that a single Coulomb of charge would experience at that location. For example, a field strength of 100 N/C means that a one-Coulomb charge will experience a force of 100 Newtons.
The Equivalent Unit: Potential Gradient (Volts per Meter)
While the Newton per Coulomb (N/C) is derived from force, the second recognized unit for the electric field is the Volt per Meter (V/m). This unit arises from considering the electric field in terms of energy and electric potential, commonly referred to as voltage. Voltage (V) is defined as the electric potential energy per unit of charge, measured in Joules per Coulomb (J/C).
The electric field relates to how the electric potential changes over a distance, a concept known as the potential gradient. If the voltage changes rapidly over a short distance, the electric field is strong. Therefore, dividing the unit of potential (Volt) by the unit of distance (meter) yields the V/m unit for the electric field.
This perspective is often more convenient in practical applications, such as when dealing with electrical circuits or devices where voltage is the primary measurable quantity. For instance, the electric field in a parallel plate capacitor is calculated by dividing the voltage applied across the plates by the distance separating them.
Understanding the Equivalence of N/C and V/m
The two units, N/C and V/m, are completely equivalent and measure the exact same physical quantity. This equivalence is rooted in the physical relationship between force and energy, which is defined by work. Work is performed when a force causes movement over a distance, and the unit of work or energy is the Joule (J).
One Joule is defined as one Newton of force applied over one meter of distance (J = N · m). The Volt is defined as one Joule of energy per one Coulomb of charge (V = J/C). By substituting these definitions, the mathematical connection between the two electric field units becomes clear.
Starting with Volts per Meter (V/m), we replace the Volt with its equivalent (J/C), resulting in (J/C) / m. Substituting the definition of the Joule (N · m) into the equation yields (N · m / C) / m. The distance unit (m) cancels out, leaving the expression N/C. Thus, 1 V/m equals 1 N/C, confirming that both units quantify the strength of the same electric field.