Electric Field
An electric field is a vector field that exists in the region around an electric charge or a changing magnetic field, representing the electrostatic force that would be exerted per unit positive charge placed at any point in space. The field lines emanate outward from positive charges and point inward toward negative charges, with the density of field lines indicating field strength. Electric fields are central to understanding capacitors, electromagnetic waves, semiconductor devices, and the operation of all electrical equipment from simple circuits to complex communication systems.
Key Formula
E = F / q = k × Q / r²
LaTeX: E = \frac{F}{q} = \frac{kQ}{r^2}
| Symbol | Meaning | Unit |
|---|---|---|
| E | Electric field strength | N/C or V/m |
| F | Force experienced by test charge | N |
| q | Test charge placed at the point | C |
| k | Coulomb's constant (8.988 × 10⁹) | N·m²/C² |
| Q | Source charge creating the field | C |
| r | Distance from source charge to point | m |
Worked Example
Problem
A positive point charge Q = +5 μC is placed in vacuum. Calculate the electric field strength at a point 0.4 m away from the charge, and find the force on a +2 μC test charge placed at that point.
Solution
Step 1: Calculate electric field at r = 0.4 m from Q. E = k × Q / r² E = (8.988 × 10⁹) × (5 × 10⁻⁶) / (0.4)² E = (8.988 × 10⁹ × 5 × 10⁻⁶) / 0.16 E = 44940 / 0.16 = 2.809 × 10⁵ N/C Step 2: Force on test charge q = 2 × 10⁻⁶ C. F = E × q = 2.809 × 10⁵ × 2 × 10⁻⁶ = 0.5618 N Direction: away from Q (both charges positive, repulsive).
Answer
E ≈ 2.81 × 10⁵ N/C; F ≈ 0.56 N (repulsive)
Electric Field Patterns for Common Charge Configurations
| Configuration | Field Pattern | Formula | Direction |
|---|---|---|---|
| Single positive point charge | Radially outward | E = kQ/r² | Away from charge |
| Single negative point charge | Radially inward | E = kQ/r² | Toward charge |
| Two parallel plates (capacitor) | Uniform between plates | E = V/d | From + to − plate |
| Electric dipole | Complex curved field lines | E = kp/r³ | Varies with position |
| Infinite line charge | Radially outward from line | E = λ/(2πε₀r) | Perpendicular to line |
Interactive Tools
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Related Terms
Electric Charge
Electric charge is a fundamental intrinsic property of matter that causes particles to experience a force when placed in an electromagnetic field, existing as either positive (carried by protons) or negative (carried by electrons) with an elementary charge unit of e = 1.602 × 10⁻¹⁹ coulombs. Charge is conserved in all physical processes (the total charge of an isolated system remains constant), and it is quantised, meaning any observable charge is an integer multiple of the elementary charge. Electric charge is the source of the electric force, which is described by Coulomb's Law and governs all electromagnetic interactions in nature and technology.
Coulomb's Law
Coulomb's Law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them, with the force acting along the line joining the charges. Formulated by Charles-Augustin de Coulomb in 1785 through careful torsion balance experiments, it is the electrostatic analogue of Newton's Law of Universal Gravitation and forms the cornerstone of classical electrostatics. The law governs the forces responsible for atomic bonding, molecular structure, and the operation of capacitors and electrostatic devices.
Electric Potential
Electric potential at a point in space is the amount of electric potential energy per unit positive test charge at that location, representing the work done per unit charge to bring a positive test charge from infinity to that point against the electric field. It is a scalar quantity measured in volts (V), where 1 volt equals 1 joule per coulomb. Electric potential is fundamental to understanding capacitors, batteries, and electrical circuits, and the difference in electric potential between two points (voltage) drives the flow of electric current.
From Latin "electricus" (produced from amber by friction) and Old English "feld" (open land, plain). The concept was introduced by Michael Faraday in the 1830s as "lines of force" to describe the region of influence around charges, later formalised mathematically by James Clerk Maxwell.