Magnetic Force on Wire Calculator

Magnetic Force on Wire Calculator
F = B × I × L × sin(θ)
Fmax = BIL (at θ=90°)
Force on a Current-Carrying Wire in a Magnetic Field
B Magnetic Field
I Current
L Wire Length in Field
θ Angle (wire to field)
90° = perpendicular (max force)
Enter B, I, L and angle
Magnetic Force Results
Force F
—
N
Fmax (at 90°)
—
N
sin(θ)
—
 
F = BIL sin(θ) — Motor Effect I F B × × × B × × × Force is perpendicular to both current and field (Fleming’s Left Hand Rule)

Figure 1: A wire carrying current I in a magnetic field B experiences a force F perpendicular to both. The force is maximum when the wire is perpendicular to the field (θ = 90°) and zero when parallel (θ = 0°).

Table of Contents
Fundamentals
  1. What Is the Motor Effect?
  2. The Force Formula
Worked Examples
  1. DC Motor Armature
  2. Loudspeaker Voice Coil
  3. Rail Gun
Deep Dive
  1. Fleming’s Left Hand Rule
  2. Applications
Reference
  1. Frequently Asked Questions
  2. Related Circuit Analysis Calculators

What Is the Motor Effect?

When a conductor carrying electric current is placed in a magnetic field, it experiences a mechanical force. This is the motor effect — the fundamental principle behind electric motors, loudspeakers, galvanometers, and many actuators. The force is perpendicular to both the current direction and the magnetic field direction.

The Induced Current Calculator covers the reverse effect: a moving conductor in a magnetic field generates an EMF (Faraday’s law). Together, the motor effect and electromagnetic induction are the two sides of electromagnetism that power the modern world.

The Force Formula

F = B × I × L × sin(θ)
Where B = magnetic field strength (T), I = current (A), L = wire length in field (m), θ = angle between wire and field.
Maximum at θ = 90° (perpendicular), zero at θ = 0° (parallel).

Worked Example — DC Motor Armature

Given: B = 0.5 T, I = 10 A, L = 0.1 m (armature conductor), θ = 90°

F = 0.5 × 10 × 0.1 × 1 = 0.5 N per conductor

With 100 conductors in the armature, total force = 50 N, producing useful torque.

Worked Example — Loudspeaker Voice Coil

Given: B = 1 T (strong permanent magnet), I = 2 A (peak audio), L = 5 m (total coil wire), θ = 90°

F = 1 × 2 × 5 × 1 = 10 N

This force pushes the speaker cone, producing sound. The Circuit Current Calculator can find the voice coil current from the amplifier voltage and coil impedance.

Worked Example — Rail Gun

Given: B = 5 T, I = 1 MA (1,000,000 A), L = 0.5 m, θ = 90°

F = 5 × 1000000 × 0.5 = 2.5 MN (250 tonnes force!)

Extreme currents and fields produce enormous forces. Electromagnetic launchers exploit this to accelerate projectiles to hypersonic speeds.

Fleming’s Left Hand Rule

Fleming’s Left Hand Rule gives the direction of force: point your first finger along the field (B), your second finger along the current (I), and your thumb shows the direction of force (F). All three are mutually perpendicular. This rule applies to conventional current (positive to negative). The Magnetic Force Between Wires Calculator uses the same electromagnetic principle but for the interaction between two current-carrying conductors.

Applications

The motor effect powers DC and AC motors, stepper motors, voice coil actuators (hard drives, speakers), solenoids, relays, MRI gradient coils, particle accelerator magnets, and electromagnetic brakes. In every case, current through a conductor in a magnetic field produces controlled mechanical motion. The Power Dissipation Calculator helps check the thermal limits of the current-carrying conductors.

Frequently Asked Questions

Why does the force depend on the angle?
Only the component of current perpendicular to the field produces force. When the wire is parallel to the field (θ = 0°), there is no perpendicular component and no force. At 90°, all the current contributes to force. This is expressed by the sin(θ) factor.
Does a stationary wire in a static field experience force?
Only if current flows through it. A stationary wire with no current in a static field experiences no force. The force requires both current AND a magnetic field.
What is the Lorentz force?
The Lorentz force F = qv × B is the force on a single moving charge in a magnetic field. When many charges move together (as current in a wire), the sum of individual Lorentz forces gives F = BIL sin(θ). It is the same physics at different scales.
Can this force do work?
Yes. The force moves the conductor, doing mechanical work. This is how electric motors convert electrical energy to mechanical energy. The electrical power input equals the mechanical power output plus losses (heat from resistance).
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Last updated: March 2026