Magnetic Force on a Wire Calculator
Calculate the force experienced by a wire carrying current through a magnetic field. Essential for understanding motors and electromagnetism.
F = B × I × L × sin(θ)
Earth's field: ~50 μT, MRI: 1.5-3 T
90° = maximum force, 0° = no force
About Magnetic Force:
When a current-carrying wire is placed in a magnetic field, it experiences a force perpendicular to both the current direction and the magnetic field. This principle is used in electric motors and loudspeakers.
How the Magnetic Force on Wire Calculator Works
Enter the current flowing through the wire, the length of wire in the magnetic field, the magnetic field strength, and the angle between the current direction and magnetic field.
The calculator applies the magnetic force formula: F = BIL sin(θ), where B is magnetic field strength, I is current, L is wire length, and θ is the angle between current and field directions. Maximum force occurs at 90° (perpendicular).
Results show the force magnitude in newtons. The direction is determined by the right-hand rule (shown in a diagram). Calculation steps display the formula with your values substituted.
When You'd Actually Use This
Electric motor design
Calculate force on motor windings. Current-carrying coils in magnetic fields experience torque. This force drives motor rotation.
Loudspeaker analysis
Understand speaker operation. Audio current in the voice coil creates force that moves the cone, producing sound waves.
Railgun calculations
Analyze electromagnetic projectile accelerators. Massive current through rails creates magnetic force that accelerates the projectile to high speeds.
Galvanometer and ammeter design
Design current-measuring instruments. Magnetic force on a coil deflects a pointer proportional to current. Foundation of analog meters.
Magnetic levitation systems
Calculate lifting force in maglev systems. Current in guideway coils creates magnetic force that levitates and propels trains.
Physics education demonstrations
Demonstrate motor effect in classrooms. A wire jumping between magnet poles when current flows shows the force dramatically.
What to Know Before Using
Force is maximum when perpendicular.sin(90°) = 1 gives maximum force. Parallel wire (θ = 0°) feels no force. Angle dramatically affects the force magnitude.
Direction follows right-hand rule.Point fingers in current direction, curl toward field direction. Thumb points in force direction. Force is perpendicular to both I and B.
Force acts on the wire, not the field.The magnetic field exerts force on moving charges (current). By Newton's third law, the wire exerts equal opposite force on the magnet.
Only the perpendicular component matters.F = BIL sin(θ) = (B sin θ)IL. Only the component of B perpendicular to the wire contributes to force.
Pro tip: For a current loop in uniform field, net force is zero but there's a torque. This torque rotates electric motor armatures. Force on opposite sides of the loop are equal and opposite, creating a couple.
Common Questions
Why is there no force when wire is parallel to field?
Magnetic force acts perpendicular to both current and field. When they're parallel, there's no perpendicular direction - the cross product is zero.
What's the unit of magnetic field?
Tesla (T) in SI. 1 T = 1 N/(A⋅m). Earth's field is ~50 μT. Strong magnets are 1-10 T. MRI machines use 1.5-7 T fields.
Does the wire material matter?
Not for the force calculation - only current matters. But material affects resistance, which determines how much current flows for a given voltage.
What if the field isn't uniform?
Integrate F = I ∫(dl × B) along the wire. For simple non-uniform fields, divide the wire into segments and sum the forces.
Can this force do work?
The magnetic force itself doesn't do work on charged particles (force is perpendicular to motion). But it can do work on the wire as a whole.
How is this related to Lorentz force?
This is the macroscopic version. Lorentz force F = q(v × B) acts on individual charges. Sum over all moving charges gives F = I(L × B).
What happens with AC current?
Force oscillates at twice the AC frequency (since force depends on current magnitude, not direction). This causes the hum in transformers.
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