ElectroHub

Magnetic Force Calculator (Lorentz Force)

A magnetic field pushes sideways on moving charge. Applied to a wire it gives F = BIL sin θ — the force that turns every motor. Applied to a free charge it gives F = qvB, which bends beams in a CRT and confines plasma.

Magnetic Force (Lorentz)

Force on a current-carrying conductor in a magnetic field — the principle behind every motor: F = B·I·L·sin θ.

Force on conductor
  1. 1.Given: B = 500 mT, I = 10 A, L = 200 mm, θ = 90°
  2. 2.FormulaF = B·I·L·sin θSubstituteF = 0.5 × 10 × 0.2 × sin 90°ResultF = 1 N
Common trap: The force is maximum when the current (or velocity) is perpendicularto the field (θ = 90°) and zero when parallel (θ = 0°). Use Fleming's left-hand rule for the direction — it's always at right angles to both the current and the field.

The formula

F = B × I × L × sin θ (conductor) ; F = q × v × B × sin θ (moving charge)

F
force (newtons)
B
flux density (tesla)
I
current in the conductor (amperes)
L
length of conductor in the field (metres)
θ
angle between the conductor and the field

Worked example

A 0.2 m conductor carrying 10 A, at right angles to a 0.5 T field.

  1. θ = 90°, so sin θ = 1
  2. F = B × I × L × sin θ = 0.5 × 10 × 0.2 × 1

F = 1 N, acting perpendicular to both the current and the field.

Where you'll use it

Motor torque, moving-coil meters and loudspeakers. Note the sin θ term: a conductor lying along the field feels no force at all, which is why motor windings are placed across the field, not along it.

The laws behind it

Parts this applies to

Motor Driver IC (L298 etc)DC MotorStepper MotorServo MotorBuzzer / PiezoSpeaker / MicrophoneHall-Effect SensorAccelerometer / Gyro / IMU

Related calculators

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