Magnetic Force on Current-Carrying Wire Calculator

When a current-carrying wire sits inside a magnetic field, the field pushes on it — a principle behind electric motors and many electromagnetic devices. Enter your Magnetic Field Strength (B), Electric Current (I), Wire Length (l), and the Angle Between Wire and Field (α) into the Magnetic Force on Current-Carrying Wire Calculator to find the Magnetic Force (F) in Newtons. Secondary outputs include Force per Unit Length, sin(α), and the Max Possible Force at a 90° angle.

T

Magnetic flux density in Tesla

A

Current flowing through the wire in Amperes

m

Length of the wire segment inside the magnetic field in meters

°

Angle in degrees between the wire direction and the magnetic field. Maximum force occurs at 90°.

Results

Magnetic Force (F)

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Force per Unit Length (F/l)

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sin(α)

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Max Possible Force (at 90°)

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Results Table

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Frequently Asked Questions

What is the formula for magnetic force on a current-carrying wire?

The magnetic force is calculated using F = BIl·sin(α), where B is the magnetic field strength in Tesla, I is the current in Amperes, l is the wire length in meters, and α is the angle between the wire and the magnetic field. The sin(α) factor accounts for the directional relationship between the current and the field.

When can we observe electromagnetic force on a wire?

An electromagnetic force acts on a wire whenever it carries electric current and is placed within a magnetic field. The wire will physically move if the magnetic force exceeds any opposing forces such as gravity or friction. This is the fundamental principle behind electric motors.

What happens when the angle α is 90°?

When α = 90°, the wire is perpendicular to the magnetic field, and sin(90°) = 1, producing the maximum possible force. This is the orientation used in most motor designs to maximize the torque and force output from a given current and field strength.

What happens when the angle α is 0° or 180°?

When α = 0° or 180°, the wire is parallel to the magnetic field, and sin(0°) = sin(180°) = 0. This means no magnetic force is exerted on the wire at all, regardless of how much current flows through it or how strong the field is.

What is the direction of the magnetic force on the wire?

The direction of the force is given by the right-hand rule (or equivalently by the cross product F = Il × B). Point your fingers along the current direction, curl them toward the magnetic field direction, and your thumb points in the direction of the force. The force is always perpendicular to both the wire and the field.

Why does a current-carrying wire experience a force in a magnetic field?

Electric current consists of moving charged particles (electrons). Each moving charge in a magnetic field experiences a Lorentz force. When summed over all the billions of electrons in the wire, this results in a net macroscopic force on the wire itself. This is essentially the Lorentz force applied at the conductor level.

What are the units used in this calculation?

Magnetic field B is measured in Tesla (T), current I in Amperes (A), wire length l in meters (m), and the resulting force F is in Newtons (N). One Newton equals one kg·m/s², and one Tesla equals one kg/(A·s²).

What are practical applications of this formula?

This formula is the foundation of electric motors, galvanometers, loudspeakers, and rail guns. Any device that converts electrical energy into mechanical motion relies on the force exerted on current-carrying conductors in magnetic fields. Understanding this force is essential in electrical engineering and physics.