Formulas & tables/Physics/Magnetism and induction/Force on a current-carrying conductor

Force on a current-carrying conductor

F=BIlsin⁡αF=BIl\sin\alpha

Result unit: N (newton)

What it describes

The force acting on a current-carrying conductor placed in a magnetic field.

Symbols

FF
force on the conductor
[N]
BB
magnetic flux density
[T]
II
current
[A]
ll
length of the conductor
[m]
α\alpha
angle between the conductor and BB
[°]

Where it comes from

A current-carrying conductor in a magnetic field is pushed out — it is the sum of the Lorentz forces acting on the charges moving in it. The basis of electric motors.

When to use it

Electric motors, loudspeakers. Maximum when the conductor is perpendicular to the field.

Example

A conductor l=0.2l=0.2 m carrying current I=5I=5 A in a field B=0.4B=0.4 T (perpendicular). Calculate the force.
SubstitutionB=0.4B=0.4, I=5I=5, l=0.2l=0.2, α=90∘\alpha=90^\circ.
ResultF=0.4⋅5⋅0.2=0.4F=0.4\cdot5\cdot0.2=0.4 N.

Related formulas

Lorentz force Induced EMF (Faraday's law)

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