How are electric potential and electric field strength related?

Electric potential and electric field strength are closely related quantities in the study of electricity. The relationship between them can be understood by examining the concept of work.

The electric field strength at a specific point in space is a vector quantity that represents the force experienced by a positive test charge placed at that point. It is denoted by the symbol E and is measured in units of Newtons per Coulomb (N/C).

On the other hand, electric potential is a scalar quantity that describes the electric potential energy per unit charge at a given point in an electric field. It is denoted by the symbol V and is measured in units of Volts (V).

The relationship between electric potential (V) and electric field strength (E) is given by the equation:

V = E × d

where V is the electric potential, E is the electric field strength, and d is the distance over which the potential is being measured.

To understand this relationship, let's consider a simple example. Suppose we have a positive test charge (+q) placed in an electric field created by a fixed source charge (+Q). The electric field exerts a force on the test charge, and if allowed to move, the test charge would experience a change in potential energy.

The work done in moving the test charge from one point to another is equal to the change in potential energy of the test charge. This work done per unit charge is defined as the electric potential difference between the two points. This potential difference depends on the electric field strength and the distance between the points.

Therefore, the electric field strength (E) can be calculated as the rate of change of electric potential (V) with respect to distance (d):

E = ΔV/Δd

In other words, the electric field tells us how the electric potential changes with distance. It provides a measure of the force per unit charge experienced by a test charge at a particular location.

Keep in mind that the above explanation assumes a uniform electric field. In more complex situations, where the electric field is non-uniform, the relationship between electric potential and electric field strength becomes more intricate and is described using calculus methods.