Formulas & tables/Physics/Magnetism and induction/Lorentz force

Lorentz force

F=qvBsin⁡αF=qvB\sin\alpha

Result unit: N (newton)

What it describes

The force acting on a charge moving in a magnetic field.

Symbols

FF
Lorentz force
[N]
qq
charge
[C]
vv
velocity
[m/s]
BB
magnetic flux density
[T]
α\alpha
angle between vv and BB
[°]

Where it comes from

A magnetic field acts only on moving charges, and perpendicular to their velocity — so it bends the particle's path (circular or spiral motion) without changing its energy.

When to use it

Motion of charges in a magnetic field; accelerators, cathode-ray tubes. Maximum for α=90∘\alpha=90^\circ.

Example

An electron (q=1.6⋅10−19q=1.6\cdot10^{-19} C) moves at v=106v=10^{6} m/s perpendicular to a field B=0.1B=0.1 T. Calculate the force.
Substitutionq=1.6⋅10−19q=1.6\cdot10^{-19}, v=106v=10^{6}, B=0.1B=0.1, α=90∘\alpha=90^\circ.
ResultF=1.6⋅10−19⋅106⋅0.1≈1.6⋅10−14F=1.6\cdot10^{-19}\cdot10^{6}\cdot0.1\approx1.6\cdot10^{-14} N.

Related formulas

Force on a current-carrying conductor Electric field strength

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