Lorentz force

Lorentz's law is a law discovered by the Dutch physicist Hendrik Antoon Lorentz. Lorentz's law defines force that acts on moving charged particles in an electromagnetic field. Force consists of magnetic force and electric force.

F = qE (electric force)
If the charge is positive, the direction of the electric force is equal to direction of electric field.

F = qv*B (magnetic force)
The direction of the magnetic force is given by the right hand rule.

If charged particles move with velocity v in an electric field E and a magnetic field B

F = qE + qv*B
F : force (vector)
q : charge (scalar)
E : electric field (vector)
v : velocity of particle (vector)
B : magnetic field (vector)
* is vector cross product.

Using this law, J.J. Thomson measured mass-to-charge ratio.

Lorentz Force Media

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  Lorentz force acting on fast-moving charged particles in a bubble chamber. Positive and negative charge trajectories curve in opposite directions.

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  Lorentz force F on a charged particle (of charge q) in motion (instantaneous velocity v). The E field and B field vary in space and time.

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  Lorentz force (per unit 3-volume) f on a continuous charge distribution (charge density ρ) in motion. The 3-current density J corresponds to the motion of the charge element dq in volume element dV and varies throughout the continuum.

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  Lorentz' theory of electrons. Formulas for the Lorentz force (I, ponderomotive force) and the Maxwell equations for the divergence of the electrical field E (II) and the magnetic field B (III), La théorie electromagnétique de Maxwell et son application aux corps mouvants, 1892, p. 451. V is the velocity of light.

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  Charged particle drifts in a homogeneous magnetic field. (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (e.g. gravity) (D) In an inhomogeneous magnetic field, grad H

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  Right-hand rule for a current-carrying wire in a magnetic field B

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  Lorentz force -image on a wall in Leiden