Fundamentals of Electric Fields and Potentials

Understanding Electric Fields and Potentials

Electric Field

The spatial region where electric forces are produced and exerted.

Electric Field Intensity

Defined as the force experienced by a positive test charge placed under the action of such a field, divided by the value of the charge.

Charged Particle Motion in Uniform Electric Fields

When a point charge of magnitude "q" enters a region where an electric field exists, it will be subjected to a force of magnitude F = qE. If the particle has mass m, the acceleration, a, imparted to it is given by a = F / m = qE / m. This relationship provides both the magnitude and the direction of the acceleration of a particle in an electric field. The magnitude is equal to qE / m, while the direction depends on the sign of the charge. If positive, the acceleration will have the same direction as E. The acceleration given by this relationship may be variable or constant, depending on the value of the electric field E. For example, if it is the field of a point charge, the expression is E = kQ/r² ⋅ û_r, where û_r is a radial unit vector which determines the direction of the electric field.

Charge Redistribution in Electrical Conductors

A good electrical conductor is a material in which electrons in the outer orbit of the atoms can move very freely within the atomic structure. Metals are examples of good conductors. When a neutral metal, inside which there are no excess charges, is inserted into an electric field, free electrons immediately move under the action of the field. Forces are exerted on the electrons that make them migrate in a direction opposite to the field. This action is very fast and occurs typically within approximately 1 µs, after which charge adjustment ceases. At this point, the conductor is said to be in electrical balance.

Electric Potential

It is defined as the potential at a point in an electric field, representing the work required to transport a unit positive charge from infinity to that point. The electric potential is a scalar quantity and can take both positive and negative values.

Electric Potential Difference

It is defined as the potential difference between two points, A and B, in an electric field. It represents the work per unit charge that an external agent has to perform to bring a unit positive charge from A to B without changing its kinetic energy. The potential difference between two points in a given electric field does not vary regardless of the path that the charge follows in its motion; i.e., it is path independent.