Formula & Calculator
Magnetic Force on a Current-Carrying Wire
The force experienced by a current-carrying conductor placed in a magnetic field.
Interpretation
Magnetic force on a straight current‑carrying wire in a uniform field is F = B·I·L·sinθ, where θ is the angle between the wire and the field.
The force is zero when the wire is parallel to the field, and maximum when perpendicular.
Example: B=0.5T, I=10A, L=0.2m, θ=90° → F = 0.5 × 10 × 0.2 × 1 = 1 N.
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
Frequently Asked Questions
The force on a straight wire in a magnetic field is F = B·I·L·sin θ, where θ is the angle between the wire and the field.
Given by the right-hand rule: F = I (L × B).
If the wire is straight and the field is uniform, the force is F = I L B sinθ.
F/L = μ₀ I₁ I₂ / (2πd) (attractive if currents in same direction).
Maximum when θ = 90° (wire perpendicular to B), zero when parallel.
Newtons (N) when B in tesla, I in amperes, L in meters.
The force on coils in a magnetic field produces torque, causing rotation.
F = q v × B; for a wire, this is the sum of forces on individual charges.
Motors, generators, loudspeakers, magnetic levitation, and railguns.
Common errors include: 1) using the wrong angle, 2) forgetting the cross product direction, 3) using the wrong units, 4) applying to a wire not in a uniform field, and 5) confusing with force on a moving charge.