Magnetic interaction
What is a magnetic field?
A magnetic field is a region where moving electric charges, electric currents, and magnetic materials can experience magnetic forces.
Magnetic field strength is commonly represented by the symbol B and is measured in teslas. This calculator determines field magnitude using two standard physics models.
Moving charged particle
Magnetic force formula
F = qvB sinθ
- F is magnetic force in newtons.
- q is charge magnitude in coulombs.
- v is particle velocity in metres per second.
- B is magnetic field strength in teslas.
- θ is the angle between velocity and field direction.
Rearranging this equation allows the calculator to solve for magnetic field, force, charge, velocity, or the acute angle.
Current-carrying conductor
Magnetic field around a straight wire
B = μ₀I ÷ 2πr
- B is magnetic field strength in teslas.
- μ₀ is vacuum permeability.
- I is current in amperes.
- r is perpendicular distance from the conductor in metres.
The field becomes stronger when current increases and weaker as the observation point moves farther from the wire.
Worked example
Calculate magnetic field around a wire
Suppose a long straight wire carries a current of 10 A, and the field is measured 0.05 m from the wire.
- Use B = μ₀I ÷ 2πr.
- Substitute μ₀ = 4π × 10⁻⁷, I = 10, and r = 0.05.
- The magnetic field is approximately 0.00004 T.
Direction matters
How angle affects magnetic force
Magnetic force depends on sinθ. At 90 degrees, the force reaches its maximum value. At 0 or 180 degrees, the particle moves parallel to the field and the magnetic force is zero.
This calculator accepts angles greater than 0 degrees and less than 180 degrees. It reports the principal acute angle when solving inversely.
SI unit guidance
Magnetic field units
- Magnetic field: teslas (T).
- Magnetic force: newtons (N).
- Charge: coulombs (C).
- Velocity: metres per second (m/s).
- Current: amperes (A).
- Distance: metres (m).
- Angle: degrees (°).
Model limitations
Assumptions and limitations
- Calculations use positive magnitudes rather than vector directions.
- The moving-charge formula assumes classical particle motion.
- The straight-wire model assumes a long, thin, straight conductor.
- Nearby magnetic materials and other field sources are not included.
Common questions
Magnetic field calculator FAQ
What formulas does the magnetic field calculator use?
For a moving charge, it uses F = qvB sinθ. For a long straight current-carrying conductor, it uses B = μ₀I/(2πr).
What is the SI unit of magnetic field strength?
Magnetic field strength, or magnetic flux density, is measured in teslas, written T.
How do I calculate magnetic field from force?
Divide magnetic force by charge, velocity, and the sine of the angle using B = F/(qv sinθ).
When is magnetic force greatest?
Magnetic force is greatest when the charged particle moves perpendicular to the magnetic field, so θ equals 90 degrees and sinθ equals 1.
Does the straight-wire formula work for every conductor?
No. It assumes a long, straight conductor in a uniform medium and calculates the field at a perpendicular distance from the wire.