Physical Significance of Electric Field

Why Introduce the Electric Field?

In electrostatics, you can always find the force on a charge directly using Coulomb’s law and the superposition principle. So why define an intermediate quantity called the electric field? The answer is twofold:

• Convenience: The electric field is an elegant way to describe the electrical environment created by a system of charges. It tells you the force a unit positive test charge would experience if placed at any point, without disturbing the original system.
• Physical necessity: The true significance of the field emerges when charges are in motion. Forces between moving charges do not act instantaneously — information travels at the speed of light $c$. The field picture explains this: an accelerated charge produces electromagnetic waves that propagate at $c$, reach another charge, and then exert a force. The field accounts for the time delay.

Thus, electric and magnetic fields are not just mathematical constructs — they are physical entities with their own dynamics, capable of transporting energy.

Definition of Electric Field

The electric field $\mathbf{E}$ at a point in space due to a system of charges is defined as the force $\mathbf{F}$ experienced by a unit positive test charge $q_0$ placed at that point, divided by $q_0$:

• $\mathbf{E}$ is a vector field — it has a magnitude and direction at every point in space.
• It is a characteristic of the source charges and is independent of the test charge used to measure it.
• For a system of point charges, the total electric field at a point is the vector sum of the fields due to each individual charge (superposition principle).

Electric Field Due to a Point Charge

For a single point charge $q$, the electric field at a distance $r$ from it is:

where: …