Electric Field - Physical Significance of Electric Field

Coulomb's Law works well for stationary charges. But it assumes force acts instantaneously — which is not possible in reality, since nothing travels faster than light.

After a time delay, the concept of the electric field was introduced to explain this delay. The idea was first proposed by Michael Faraday through his concept of "lines of force."

A time-dependent combination of electric and magnetic fields that propagates through space and can transport energy is called an electromagnetic field.

Electric Field \[\vec E\] at a point is the electrostatic force \[\vec F\] experienced by a vanishingly small positive test charge q₀ placed at that point:

\[\vec E\] = \[\frac {\vec F}{q_0}\]

Case A: Static Charges

When all charges are at rest, the electric field:

• Describes the electrical environment around a charge system
• Gives the force per unit positive charge at any point
• Is constant in time
• Can be fully calculated using Coulomb's Law + Superposition Principle

In this case, the field is a convenient descriptive tool — similar to the gravitational field g, which describes the force per unit mass near Earth.

Case B: Accelerated Charges

When a charge is accelerated, something more important happens:

• The accelerated charge generates electromagnetic waves
• These waves travel at the speed of light, c = 3 × 10⁸ m/s
• The second charge q₂ feels the effect only after time Δt = d/c

This proves the electric field is not just a mathematical tool — it is a real physical entity that carries energy and propagates through space.

Static vs. Time-Varying Field

• Energy Storage: Electric field between the capacitor plates stores measurable energy
• Energy Transport: EM waves carry energy from a source to a receiver (e.g., sunlight reaching Earth)
• Independent Existence: Even after the source charge is removed, the EM wave continues to travel
• Momentum: EM fields carry momentum — this is why solar sails on spacecraft work

Problem: An electron falls through 1.5 cm in a uniform electric field of 2.0 × 10⁴ N C⁻¹. Find the time of fall. (Neglect gravity.)

Formula:

t = \[\sqrt {\frac {2hm}{qE}}\]

For electron (m_e = 9.1 × 10⁻³¹ kg):

t_e = \[\sqrt{\frac{2\times1.5\times10^{-2}\times9.1\times10^{-31}}{1.6\times10^{-19}\times2.0\times10^{4}}}\approx2.9\times10^{-9}\mathrm{s}\]

For proton (mp = 1.67 × 10⁻²⁷ kg):

tp ≈ 1.25 × 10⁻⁷ s

The electric acceleration of electron ≈ 3.5 × 10¹⁵ m s⁻², which is ~ 10¹⁴ times greater than g. Gravity is negligible.

• \[\vec E\] = \[\vec F\]/q₀ — force per unit positive test charge
• Static case → Coulomb's Law is sufficient; field is a descriptive tool
• Accelerated charges → field becomes a real physical entity (EM waves)
• Time delay = d/c — information travels at the speed of light, not instantaneously
• An electric field carries and transports energy
• Field exists independently of whether any test charge is present
• Gravity is negligible for charged particles in typical electric fields