Electric Field Calculator — E=kq/r²
Calculate electric field strength using E = F/q and E = kq/r² (Coulomb's law).
E = kq / r² (Coulomb's law for electric field)
What Is the Electric Field Calculator — E=kq/r²?
The Electric Field Calculator computes the electric field strength produced by a point charge at a given distance, using Coulomb's law. It also calculates the force on a test charge in a known field and the field between parallel plates given a voltage and separation distance.
Formula
How to Use
To find the field from a point charge: enter the source charge Q (in coulombs) and the distance r from the charge. To find the field between parallel plates: enter the voltage difference and plate separation. The calculator returns field strength in N/C (or V/m) and the force on a test charge.
Example Calculation
Point charge Q = 2×10⁻⁶ C at r = 0.5 m: E = (8.99×10⁹ × 2×10⁻⁶) / 0.5² = 17,980 / 0.25 = 71,920 N/C. Parallel plates with V=100V, d=0.01m: E = 100/0.01 = 10,000 V/m.
Understanding Electric Field — E=kq/r²
The electric field is a vector field that describes the force per unit positive charge at every point in space. Produced by electric charges, it is fundamental to understanding electrostatics, capacitors, electromagnetic induction, and the behaviour of charged particles in accelerators and detectors.
Coulomb's law gives the field from a single point charge: E = kQ/r², which falls off as the square of distance. For multiple charges, the principle of superposition applies — the total field is the vector sum of fields from each individual charge. This principle underlies the calculation of fields in complex charge distributions.
Electric fields are essential in capacitor design, where parallel plate geometry creates a uniform field for energy storage. They also govern the operation of cathode ray tubes, particle accelerators, ink-jet printers, and electrostatic precipitators. Understanding how to calculate field strength is a fundamental skill in both academic physics and electrical engineering.
Frequently Asked Questions
What are the units of electric field?
Electric field has units of N/C (newtons per coulomb) or equivalently V/m (volts per meter). Both are the same unit expressed differently.
What is Coulomb's constant k?
Coulomb's constant k = 1/(4πε₀) ≈ 8.99×10⁹ N·m²/C², where ε₀ = 8.85×10⁻¹² F/m is the permittivity of free space.
What direction does the electric field point?
Electric field vectors point away from positive charges and toward negative charges. The field direction is the direction a positive test charge would accelerate.
What is a uniform electric field?
A uniform field has the same magnitude and direction everywhere. It occurs between two large, parallel, oppositely charged plates. Its strength is simply E = V/d.
Is this calculator free?
Yes, completely free with no account needed.