Electromagnetism Calculator — Force, Field, Flux

Compute electric and magnetic fields, forces on moving charges and EM induction.

About this calculator

An electromagnetism calculator handles Coulomb's law (force between charges), electric field calculations, capacitance, magnetic force on a current-carrying conductor, and Faraday's law of induction. These four problems cover the vast majority of undergraduate electromagnetism coursework.

Electromagnetic phenomena are fully described by Maxwell's equations, which are partial differential equations. The calculator handles the algebraic special cases (point charges, parallel plate capacitors, straight current-carrying wires) where the integrals reduce to simple algebraic formulas.

Formula

F = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r^2}

  • Coulomb's law — F between two point charges
  • ε₀ — 8.854 × 10⁻¹² F/m (permittivity of free space)
  • E — Electric field = F/q at a point
  • Capacitor — C = ε₀A/d for parallel plates

Worked example

Inputs: Force between two 1 µC charges separated by 1 cm

  1. Use F = kq₁q₂/r² with k = 8.99 × 10⁹ N·m²/C²
  2. F = 8.99 × 10⁹ × (10⁻⁶)² ÷ (0.01)²
  3. F = 8.99 × 10⁹ × 10⁻¹² ÷ 10⁻⁴
  4. F = 89.9 N — a substantial force for such small charges, illustrating Coulomb force's strength

Frequently asked questions

Why is gravity so much weaker than the electric force?

On a fundamental level it is a deep mystery. Numerically: the ratio of Coulomb to gravitational force between two protons is ~10³⁶ — Coulomb wins by 36 orders of magnitude. At cosmic scales gravity dominates only because matter is electrically neutral on average (equal positives and negatives cancel). One unbalanced electron in your body would attract Earth's electron with more force than gravity from your body's entire mass.

What is electromagnetic induction used for?

Faraday's law (changing magnetic flux induces voltage) powers nearly all electric generators, transformers, induction motors, wireless charging pads, induction stovetops, and metal detectors. Without electromagnetic induction, modern civilisation would not exist — there would be no efficient way to generate or distribute electric power.

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