Magnetic Force on a Current-Carrying Wire
With this magnetic force on a current-carrying wire calculator, you can estimate the magnetic force that acts on a straight wire with current flowing through it.
From a microscopic point of view, the electric current is the result of the flow of tiny charged particles — electrons. If a charged particle moves in a magnetic field, it will be subjected to the Lorentz force. Below, we explain how you can estimate the force acting on a straight wire with about 10¹² electrons moving through it. Be sure to also check our magnetic field of a straight wire calculator and the solenoid magnetic field calculator.
When can we observe electromagnetic force?
When we place a wire that carries an electric current in a magnetic field, each of the moving electrons (which comprise the current) will experience the Lorentz force (see our Lorentz force calculator for more details). It means that this wire will start moving if there is no other strong enough force that can stop it — for example, a friction force. Such a condition may be met when the wire hangs vertically in the air.
💡 To learn more about frictional forces, check out our friction calculator.
Magnetic force on a straight current-carrying wire equation
Making use of some mathematical tricks to avoid using cross products, we can simplify the formula. The formula that lets you calculate the strength of the magnetic force acting on a straight current-carrying wire is simply:
F = B · I · L · sin(α)
- F — Magnetic force acting on the wire (Newtons, N);
- B — Strength of the magnetic field (Tesla, T);
- I — Current flowing through the wire (Amperes, A);
- L — Length of the wire (meters, m); and
- α — Angle between the direction of current and the direction of the magnetic field.
As we can see, the magnetic force on a current-carrying wire is an application of the cross product of two vectors.
We often assume for simplicity that α = 90° and therefore sin(α) = 1. From this formula, you can see that if the directions of the current and the magnetic field are parallel (α = 0°), the resulting force is zero. On the other hand, the highest possible electromagnetic force is achievable when those directions are perpendicular (α = 90°).
How to use the calculator
- Choose your unit system — metric (SI) or the American system of measurement.
- Enter the magnetic field strength B (in μT, mT, T, or Gauss).
- Enter the electric current I (in mA, A, or kA).
- Enter the length of the wire L (in mm, cm, m, inches, or feet).
- Enter the angle α between the current and the magnetic field (0°–180°). Leave it at 90° for the maximum force.
- The calculator applies F = B × I × L × sin(α) and reports the force in newtons (N), millinewtons (mN), kilonewtons (kN), dynes (dyn), and pounds-force (lbf).
What next?
Once you know the force on a single wire, you may want to explore the magnetic force between two parallel wires, the magnetic field produced by a straight wire, or the field inside a solenoid. Magnetic forces like this are the working principle behind electric motors, loudspeakers, and the moving-coil galvanometer.
Unit conversions
- 1 N = 1,000 mN = 0.001 kN = 100,000 dyn ≈ 0.224809 lbf
- 1 T = 1,000 mT = 1,000,000 μT = 10,000 G
- 1 in = 0.0254 m; 1 ft = 0.3048 m
Frequently Asked Questions
When is the magnetic force on a wire at its maximum?
The force is greatest when the wire is perpendicular to the magnetic field (α = 90°), because sin(90°) = 1. As the wire becomes more aligned with the field, the force decreases, reaching zero when the current flows parallel to the field (α = 0° or 180°).
Why is the force zero when the current is parallel to the field?
The magnetic force comes from the cross product of the current direction and the magnetic field. When the two vectors are parallel, their cross product is zero, so sin(α) = 0 and no force acts on the wire.
In which direction does the force act?
The direction is given by the right-hand rule: point your fingers in the direction of the current and curl them toward the magnetic field; your thumb then points in the direction of the force. The force is always perpendicular to both the current and the field.
Does this formula work for any wire shape?
The equation F = BIL·sin(α) applies to a straight segment of wire in a uniform magnetic field. For curved wires or non-uniform fields, the wire must be split into small segments and the contributions added together (integrated).