Magnetic Force on a Wire Calculator
Force on a current-carrying wire in a magnetic field: F = B · I · L · sin θ.
Inputs
Drag the handle (or focus it and press ↑/↓) to reorder. Scientific notation such as 2e-3 is accepted. Pick any unit; conversion is automatic. θ is the angle between the current direction and the field. Pick any unit; conversion is automatic.
Results
Enter values and press Calculate. Your answer will appear here.
Magnetic force vs. angle
The force follows sin θ: zero when the wire is parallel to the field, largest when it is perpendicular. The dashed line is the maximum, and the dot is your result.
What is being calculated
Reference values
| Angle θ (B = 0.5 T, I = 10 A, L = 0.2 m) | sin θ | Force F |
|---|
The force depends only on the component of B perpendicular to the wire, B·sin θ.
Typical magnetic fields for scale (approximate)
| Source | B |
|---|---|
| Earth’s surface | ≈ 25 to 65 µT |
| Fridge magnet | ≈ 5 mT |
| Clinical MRI scanner | ≈ 1.5 to 3 T |
| Strongest sustained lab magnets | ≈ 45 T |
Unit conversions
| Quantity | Conversion |
|---|---|
| Force | 1 N = 1,000 mN = 10⁵ dyn = 0.22481 lbf = 0.10197 kgf |
| Magnetic field | 1 T = 1,000 mT = 10,000 G · 1 G = 100 µT |
| Length | 1 cm = 0.01 m · 1 in = 0.0254 m · 1 ft = 0.3048 m |
| Angle | 180° = π rad · 1 rad = 57.2958° |
Formula
- F: magnetic force on the wire (N)
- B: magnetic flux density (T)
- I: current (A)
- L: length of wire inside the field (m)
- θ: angle between the current direction and B
Example: B = 0.5 T, I = 10 A, L = 0.2 m, θ = 90°. F = 0.5 × 10 × 0.2 × sin 90° = 1 N. At θ = 30° the force is half as large, 0.5 N.
In vector form F = I (L × B), so the force is perpendicular to both the wire and the field; use the right-hand rule for the direction. For N identical wire segments the force is multiplied by N. The formula is for a straight wire in a uniform field; for a curved wire or a varying field, split the wire into short pieces and add the forces. Advanced mode can solve for B, I, L or θ from a known force, and compares the force with the weight of the wire. Solving for θ gives two answers, θ and 180° − θ, because their sines are equal.
References
- Wikipedia, Lorentz force: force on a current-carrying wire
- OpenStax University Physics Vol. 2, Magnetic Force on a Current-Carrying Conductor: F = I L × B
- NIST SP 811, Guide for the Use of the SI: unit conversion factors
How to Use This Tool
- Pick a preset, or enter the magnetic field B and the current I with their units.
- Enter the length L of wire inside the field and the angle θ between the wire and B.
- In Advanced, solve for B, I, L or θ from a known force, or add the number of wires and the wire mass.
- Click Calculate.
- Read the result, then check the force-vs-angle chart.
What This Tool Offers
- Basic and Advanced modes on one calculation engine
- Field, current, length, angle and force unit conversion (N, mN, µN, kN, lbf, kgf, dyn)
- Maximum force, percentage of maximum and the perpendicular field component
- Solve for B, I, L or θ, multiple wires, and a weight and acceleration check (Advanced)
- Force-vs-angle chart and labelled wire-in-field diagram
- Reorderable inputs, presets and a mobile-friendly layout
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| F | Magnetic force on the wire | N |
| B | Magnetic flux density (external field) | T |
| I | Current flowing through the wire | A |
| L | Length of wire in the magnetic field | m |
| θ | Angle between wire (current direction) and magnetic field | ° |
What it means
A current‑carrying wire in a magnetic field experiences a force given by F = B·I·L·sinθ, where B is the magnetic field, I is the current, L is the length of wire in the field, and θ is the angle between the wire and the field. The direction is given by the right‑hand rule. This force is the basis for the operation of electric motors, galvanometers, and loudspeakers. It also explains the force between parallel current‑carrying wires. The force is zero when the wire is parallel to the field and maximum when perpendicular. Example: A wire of length 0.2m carrying 10A in a 0.5T field at an angle of 90° experiences F = 0.5 * 10 * 0.2 * 1 = 1 N. This force is used to produce torque in a motor.
Worked example
Magnetic Force on a Wire – Practical Example
Real‑World| Parameter | Value |
|---|---|
| B | 0.3 T |
| I | 5 A |
| L | 0.2 m |
| θ | 90° |
| Formula | F = B·I·L·sinθ |
Common mistakes
- Angle θ: The angle between the wire (current direction) and the magnetic field.
- Force direction: Use the right‑hand rule: I × B.
- Length L: The portion of the wire in the field – in metres.
- Units: B in teslas, I in A, L in m → F in N.
- For a coil: The net force on a closed loop in a uniform field is zero (but torque may exist).
Applications
Magnetic force on a current‑carrying wire is F = B·I·L·sinθ, where θ is the angle between the wire and the magnetic field. This is the basis for electric motors, generators, and actuators. Engineers use it to calculate the force on conductors in magnetic fields, to design motor windings, and to determine the torque on rotating machines. It is also essential for loudspeaker design, where the force on the voice coil creates sound. By applying this formula, professionals can optimise the performance of electromagnetic devices. This law is one of the key principles of electromechanical energy conversion.
- Design of electric motors, generators, and actuators
- Loudspeaker and headphone driver design
- Magnetic levitation and suspension systems
- Linear motors and conveyor systems
- Educational understanding of magnetic force
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