Electromagnetic Force Calculator

The Electromagnetic Force Calculator computes force and torque in 4 modes — force on wire in field (F=BIL), force between parallel wires (µ₀I₁I₂/2πd), Lorentz force on moving charges (F=qvB), and current loop torque (τ=NBIA) — with interactive SVG force diagrams showing right-hand rule directions. Free, no signup required.

Calculation Mode

Presets

Current (A)

Wire Length (m)

Magnetic Field (T)

Angle θ (degrees)

Results

Force

5 N

Direction

Perpendicular to both B and I (right-hand rule)

Force Diagram

Formula

F = B × I × L × sin(θ)

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What is an Electromagnetic Force Calculator?

An electromagnetic force calculator computes the mechanical force and torque produced by magnetic fields acting on current-carrying conductors and moving charges. It implements four fundamental equations: F = BIL sin(θ) for a wire in a uniform field, F/L = µ₀I₁I₂/(2πd) for parallel wires, F = qvB sin(θ) for the Lorentz force, and τ = NBIA sin(θ) for motor torque. This calculator includes interactive SVG force diagrams with right-hand rule direction visualization.

How to Use This Calculator

Select a calculation mode: wire in field, parallel wires, Lorentz force, or current loop torque
Enter the required parameters or choose a preset (power line, rail gun, cyclotron, DC motor)
View the force/torque result with direction indicator
Examine the interactive force diagram showing field, current, and force vectors
For Lorentz force mode, see the cyclotron radius and frequency for circular motion

Frequently Asked Questions

What is the force on a current-carrying wire in a magnetic field?

The force is F = BIL sin(θ), where B is the magnetic field strength, I is the current, L is the wire length, and θ is the angle between the wire and field. When the wire is perpendicular to the field (θ = 90°), the force is maximum: F = BIL. The direction follows the right-hand rule.

Do parallel wires attract or repel each other?

Parallel wires carrying current in the same direction attract each other, while wires carrying current in opposite directions repel. The force per unit length is F/L = µ₀I₁I₂/(2πd). This is the basis for the original definition of the ampere.

What is the Lorentz force and what is cyclotron motion?

The Lorentz force F = qv × B acts on a charged particle moving in a magnetic field. When the velocity is perpendicular to the field, the particle follows a circular path with radius r = mv/(qB) at cyclotron frequency f = qB/(2πm). This principle is used in particle accelerators and mass spectrometers.