The electric field is an invisible influence surrounding any object with an electric charge. This field allows one charged object to exert a force on another without physical contact. The concept describes the space around a charge, mapping out the potential forces that would act on any other charge placed within that region. Understanding the electric field requires examining the mathematical expressions that define its strength and direction.
The Foundational Formula: Force per Unit Charge
The most fundamental definition of the electric field, denoted by the symbol \(E\), is based on the force it exerts. The field strength at a specific location is defined as the electric force (\(F\)) experienced by a small, positive test charge (\(q_0\)) divided by the magnitude of that test charge. This relationship is expressed by the formula \(E = F/q_0\).
The force (\(F\)) is measured in Newtons (N), and the test charge (\(q_0\)) is measured in Coulombs (C). This definition isolates the field from the object used to measure it, ensuring the resulting value for \(E\) depends only on the source charges. The standard unit derived from this foundational relationship is Newtons per Coulomb (N/C).
Calculating the Field from a Point Source
While the foundational formula requires a test charge, a second formula calculates the field’s strength based purely on the source charge (\(Q\)). This expression finds the magnitude of the electric field (\(E\)) created by a single, static point charge. The formula is \(E = k \cdot Q / r^2\).
The variable \(r\) represents the distance from the source charge to the point where the field is being calculated. A constant of proportionality, \(k\) (Coulomb’s constant), has an approximate value of \(8.99 \times 10^9 \text{ N} \cdot \text{m}^2/\text{C}^2\). The \(r^2\) term in the denominator signifies the inverse square law, which is a common feature in many physical phenomena like gravity.
Doubling the distance (\(r\)) from the charge reduces the electric field strength to one-fourth of its original value. This expression predicts the field strength around a charge at any distance without needing a second charge to measure the force.
Alternative Expression: Linking Field to Voltage
The electric field can also be described through its relationship with electric potential, commonly known as voltage (\(V\)). Electric potential represents the potential energy per unit charge at a specific point in the field. The electric field is directly related to how quickly the voltage changes over distance.
For the specific case of a uniform electric field, such as one existing between two parallel, charged plates, the relationship is simplified to \(E = \Delta V / d\). In this formula, \(\Delta V\) is the potential difference (voltage) between the two points, and \(d\) is the distance separating them. This expression demonstrates that the electric field is essentially the potential gradient, or the voltage drop per unit distance.
This relationship introduces a second common unit for the electric field: Volts per meter (V/m). Since both the force-based definition (\(E = F/q_0\)) and the voltage-based definition (\(E = \Delta V / d\)) describe the same physical phenomenon, the units N/C and V/m are equivalent. This alternative view is often more practical in electrical engineering, as voltage and distance are easily measured.
The Directional Nature of the Electric Field
The electric field is a vector quantity, possessing both magnitude (strength) and a specific direction in space. The direction of the electric field at any point is conventionally defined as the direction a small, positive test charge would be pushed or pulled. This convention simplifies visualizing the field’s influence.
For an isolated positive source charge, field lines point radially outward. Conversely, for a negative source charge, they point radially inward. Electric field lines are a visual tool used to represent this vector nature. The arrows on these field lines indicate the field’s direction. The density of the lines represents the field’s strength: where lines are close together, the field is stronger, and where they are spread apart, the field is weaker. This visualization helps predict the path a charged particle would follow within the electric field.