Magnetic Force Calculator — Force on Moving Charges and Wires
Calculate magnetic force on a moving charge F = qvB and on current-carrying wires F = BIL. Includes field direction, Lorentz force, and motor effect examples.
Magnetism and electricity are two faces of the same phenomenon, and the magnetic force on moving charges is where they intersect most clearly. A charge sitting still in a magnetic field feels nothing. Get it moving, and suddenly a force appears — perpendicular to both the velocity and the magnetic field. This right-angle geometry is why electric motors spin and why particle accelerators curve beams.
The CalcHub magnetic force calculator computes magnetic force on charges and current-carrying conductors.
The Formulas
Force on a moving charge (Lorentz force): F = q × v × B × sin(θ) Force on a current-carrying wire: F = B × I × L × sin(θ)- F = force (Newtons, N)
- q = charge (Coulombs, C)
- v = velocity (m/s)
- B = magnetic field strength (Tesla, T)
- I = current (Amperes, A)
- L = length of wire (m)
- θ = angle between velocity/current and magnetic field
Direction: The Right-Hand Rule
Point fingers in the direction of velocity (or current for positive charge), curl them toward B — thumb points in the direction of force. For negative charges, reverse the direction.
Magnetic Field References
| Source | Typical B |
|---|---|
| Earth's surface | 25–65 μT |
| Refrigerator magnet | ~5 mT |
| MRI machine | 1.5–3 T |
| Strongest lab magnet | ~45 T |
| Neutron star surface | ~10⁸ T |
Worked Example
A proton (q = 1.6 × 10⁻¹⁹ C) moves at 5 × 10⁶ m/s perpendicular to a 0.5 T magnetic field.
F = qvB × sin(90°) = 1.6 × 10⁻¹⁹ × 5 × 10⁶ × 0.5 × 1
= 4 × 10⁻¹³ N
This tiny force is enough to curve a proton's path in a cyclotron or mass spectrometer.
Why does the magnetic force never do work?
Because it's always perpendicular to velocity. Work = F·d·cos(θ), and when θ = 90° between force and displacement, work = 0. Magnetic forces change the direction of motion but never the speed or kinetic energy. This is why charges move in circles in magnetic fields — speed stays constant, direction changes continuously.
How does an electric motor work?
A current-carrying coil in a magnetic field experiences opposing forces on its two sides (from F = BIL), creating a torque that spins the coil. As the coil rotates, a commutator reverses the current direction to maintain torque in the same rotational direction. Virtually every electric motor uses this principle.
What is the difference between magnetic flux density (B) and magnetic field strength (H)?
B (Tesla) is the magnetic flux density — what you measure with a magnetometer, and what appears in force equations. H (A/m) is magnetic field intensity. They're related by B = μ₀μ_r × H. In free space, B = μ₀H. The distinction matters in magnetic materials where permeability μ_r varies.