How to Use Magnetic Force on Current-Carrying Wire Calculator
The Magnetic Force on Current-Carrying Wire Calculator evaluates the Lorentz force on a straight conductor in a uniform magnetic field.
- Enter B — Input the magnetic flux density and choose T or mT.
- Enter I — Input the current through the wire and choose A or mA.
- Enter L — Input the length of wire inside the magnetic field and choose m, cm, or mm.
- Enter θ — Input the angle in degrees between the current direction and the magnetic field direction. The default of 90° gives the maximum force.
- Read the results — The calculator displays the force F in Newtons, the sin(θ) value used, and a contextual note about the angle.
Formula & Theory — Magnetic Force on Current-Carrying Wire Calculator
The Magnetic Force on Current-Carrying Wire Calculator is built on the standard expression for the force on a current-carrying conductor in an external magnetic field:
F = B × I × L × sin(θ)| Symbol | Meaning |
|---|---|
| F | Magnetic force (N) |
| B | Magnetic flux density (T) |
| I | Current (A) |
| L | Effective wire length in the field (m) |
| θ | Angle between current direction and B field |
This expression is derived from the Lorentz force law F = qv × B integrated over all charge carriers in the conductor.
Special Angle Cases
| θ | sin(θ) | Force |
|---|---|---|
| 0° | 0 | F = 0 (wire parallel to B) |
| 90° | 1 | F = BIL (maximum force, wire perpendicular to B) |
| 30° | 0.5 | F = 0.5 × BIL |
Direction of Force
The direction of the force is given by the right-hand rule (or left-hand rule for conventional vs electron current): point fingers in the direction of current I, curl them toward B, and the thumb points in the direction of force F.
Use Cases for Magnetic Force on Current-Carrying Wire Calculator
The Magnetic Force on Current-Carrying Wire Calculator is applicable across many physics and engineering contexts:
- Electric motors — The torque in a DC or AC motor is generated by the magnetic force on current-carrying conductors inside a magnetic field. The Magnetic Force on Current-Carrying Wire Calculator helps students understand why motor torque increases with current and field strength.
- Galvanometers and ammeters — Sensitive current-measuring instruments rely on the deflection of a coil in a magnetic field, which is directly proportional to the current via the Lorentz force formula.
- Rail guns and electromagnetic launchers — These devices accelerate a conducting projectile using the force on a current-carrying conductor. Engineers use the magnetic force formula to estimate launch energies.
- MRI and NMR — Gradient coils in MRI machines carry large currents in strong magnetic fields; knowing the resulting mechanical forces is essential for mechanical design.
- Physics lab demonstrations — Students use current-carrying wires in uniform fields (between magnet poles) to measure the force and verify the linear relationship with I, L, and sin(θ).
- Electromagnetic braking — Linear induction brakes apply a retarding force to a conductor moving through a field; the same formula applies when the conductor carries its own current.