Why is the force zero when the wire is parallel to B?

The cross product of two parallel vectors is zero. When I and B are parallel, there is no perpendicular component to create a force. The sin θ factor captures this: sin 0° = 0.

In which direction does the force act?

The force is perpendicular to both the current direction and the magnetic field, given by the right-hand rule (or F = IL × B as a cross product). It is often called the Laplace force.

How does this relate to electric motors?

In a motor, current-carrying coils in a magnetic field experience this force, creating torque. The commutator reverses current direction each half-turn to maintain rotation in one direction.

What is the difference between this and the Lorentz force?

The Lorentz force F = qv×B acts on individual charges. The wire force F = IL×B is the macroscopic sum of Lorentz forces on all the moving charges in the wire. They are fundamentally the same phenomenon.

Can this force be used for propulsion?

Yes — electromagnetic rail guns and MHD (magnetohydrodynamic) drives use the F = BIL force for propulsion. Rail guns can achieve velocities of several km/s.

Does the wire material matter?

The magnetic force depends only on current, field, and geometry — not wire material. However, the wire resistance (material-dependent) determines how much voltage is needed to sustain the current.

Magnetic Force on Wire Calculator

Calculate the force on a current-carrying wire in a magnetic field using F = BIL sin θ. Includes force-vs-angle chart and magnetic field reference table.

Current (I)

Wire Length (L)

Magnetic Field (B)

Angle θ (wire to B)

Force on Wire

0.5000 N

500.00 mN

Maximum Force (θ = 90°)

0.5000 N

F = BIL

Force per Unit Length

2.5000 N/m

F/L = BI sin θ

sin θ Factor

1.0000

θ = 90.0°

Approx. Torque

0.0500 N·m

F × L/2 (center pivot)

Force Efficiency

100.0%

sin θ as % of maximum

Force vs Angle

0°

30°

60°

90°

120°

150°

180°

Force follows sin(θ) — maximum at 90°, zero at 0° and 180°

Magnetic Field Strengths Reference

Source	Field Strength	Tesla
Earth's surface	25–65 μT	5 × 10⁻⁵
Fridge magnet	5 mT	5 × 10⁻³
Loudspeaker magnet	1 T	1
NdFeB magnet	1.2 T	1.2
MRI machine	1.5–3 T	1.5–3
Superconducting magnet	10–20 T	10–20
Magnetar surface	10⁸–10¹¹ T	~10¹⁰

Planning notes, formulas, and examples

About the Magnetic Force on Wire Calculator

When a current-carrying wire is placed in a magnetic field, it experiences a force perpendicular to both the current direction and the field — this is the principle behind every electric motor, loudspeaker, and electromagnetic actuator. The force magnitude is F = BIL sin θ, where θ is the angle between the wire and the field. At 90° the force is maximum; at 0° (wire parallel to field) the force is zero.

This Magnetic Force on Wire Calculator computes the force for any angle, current, wire length, and field strength. It visualizes the sinusoidal force-vs-angle relationship, shows force efficiency relative to the maximum, and provides a reference table of magnetic field strengths from Earth's field to superconducting magnets.

From designing electric motors to understanding rail guns, this calculator makes the F = BIL relationship interactive and visual. Physics students and electrical engineers use it for quick force estimates and to build intuition about electromagnetic forces.

When This Page Helps

The F = BIL sin θ formula is simple but remembering to include the angle factor is a common error source. This calculator handles the trigonometry, shows force at every angle graphically, and provides field-strength references — making it faster and more reliable than manual calculation for motor design, lab experiments, or homework problems.

How to Use the Inputs

Enter the current flowing through the wire in amperes.
Enter the length of wire within the magnetic field.
Enter the magnetic field strength (B) in Tesla.
Set the angle between the wire direction and the B field.
Review the force, force per unit length, and sin θ factor.
Check the force-vs-angle chart to see how orientation affects force.

Formula used

Force on a current-carrying wire:
  F = BIL sin θ

Force per unit length:
  F/L = BI sin θ

Maximum force (θ = 90°):
  F_max = BIL

Where:
  B = magnetic field strength (T)
  I = current (A)
  L = wire length in the field (m)
  θ = angle between wire and B field (degrees)

Example Calculation

Result: F = 0.5 N

A 0.2 m wire carrying 5 A perpendicular to a 0.5 T field experiences 0.5 N of force. This is the maximum force for these parameters. At 45°, the force would drop to 0.354 N (× sin 45°).

Tips & Best Practices

Maximum force occurs at θ = 90° — orient the wire perpendicular to the field for strongest force.
The formula assumes a uniform magnetic field across the entire wire length.
For curved wires in non-uniform fields, integrate dF = I(dL × B) along the wire.
In motors, the average force over a rotation is about 2/π ≈ 64% of the peak force.
Rail gun projectile velocity scales with current squared — doubling current quadruples muzzle energy.

From Wire Force to Motor Torque

The force on a single wire segment is the building block of motor design. In a DC motor, many wire segments (coil turns) rotate in a magnetic field. The torque is τ = NBIA sin θ, where N is the number of turns and A is the coil area. Commutators or electronic controllers ensure the angle stays near 90° for maximum average torque.

Electromagnetic Launchers

Rail guns exploit the F = BIL principle on a massive scale. Two parallel conducting rails carry enormous currents (100,000+ A) through a sliding armature. The armature experiences a huge force that accelerates it down the rail. Practical rail gun designs achieve projectile speeds of 2–3 km/s, with military applications for long-range precision strike.

Practical Considerations

In real systems, heating (I²R losses), field non-uniformity, and mechanical constraints limit performance. Superconducting magnets can provide very high fields (10+ T) without resistive heating, enabling compact, high-force electromagnetic devices for MRI machines, particle accelerators, and maglev trains.

Sources & Methodology

Last updated: March 7, 2026

Frequently Asked Questions

The cross product of two parallel vectors is zero. When I and B are parallel, there is no perpendicular component to create a force. The sin θ factor captures this: sin 0° = 0.