Lorentz force

(noun)

The force exerted on a charged particle in an electromagnetic field.

Related Terms

Examples of Lorentz force in the following topics:

  • Electric Motors

    • If you were to place a moving charged particle in a magnetic field, it would experience a force called the Lorentz force:
    • Therefore, a current-carrying coil in a magnetic field will also feel the Lorentz force.
    • For a straight current carrying wire that is not moving, the Lorentz force is:
    • The direction of the Lorentz force is perpendicular to both the direction of the flow of current and the magnetic field and can be found using the right-hand rule, shown in .
    • This force is the Lorentz force on the moving charges in the conductor.

  • Superposition of Forces

    • The superposition principle (superposition property) states that for all linear forces the total force is a vector sum of individual forces.
    • Therefore, the principle suggests that total force is a vector sum of individual forces.
    • Total force, affecting the motion of the charge, will be the vector sum of the two forces.
    • (In this particular example of the moving charge, the force due to the presence of electromagnetic field is collectively called Lorentz force (see ).
    • Lorentz force f on a charged particle (of charge q) in motion (instantaneous velocity v).

  • Examples and Applications

    • This frequency is given by equality of centripetal force and magnetic Lorentz force.
    • The magnetic field causes the electrons, attracted to the (relatively) positive outer part of the chamber, to spiral outward in a circular path, a consequence of the Lorentz force.
    • Equating the above expressions for the force applied to the ion yields:
    • Magnetic lines of force are parallel to the geometric axis of this structure.

  • Electric vs. Magnetic Forces

    • Force due to both electric and magnetic forces will influence the motion of charged particles.
    • The curl of the electric force is zero, i.e.:
    • The Lorentz force is the combined force on a charged particle due both electric and magnetic fields, which are often considered together for practical applications.
    • Magnetic fields exert forces on moving charges.
    • This force is one of the most basic known.

  • The Hall Effect

    • When a magnetic field is present that is not parallel to the motion of moving charges within a conductor, the charges experience the Lorentz force.
    • This opposes the magnetic force, eventually to the point of cancelation, resulting in electron flow in a straight path .
    • Initially, the electrons are attracted by the magnetic force and follow the curved arrow.
    • This force becomes strong enough to cancel out the magnetic force, so future electrons follow a straight (rather than curved) path.

  • Circular Motion

    • Magnetic forces can cause charged particles to move in circular or spiral paths.
    • Particle accelerators keep protons following circular paths with magnetic force.
    • So, does the magnetic force cause circular motion?
    • (If this takes place in a vacuum, the magnetic field is the dominant factor determining the motion. ) Here, the magnetic force (Lorentz force) supplies the centripetal force
    • The Lorentz magnetic force supplies the centripetal force, so these terms are equal:

  • A Quantitative Interpretation of Motional EMF

    • A a motional EMF is an electromotive force (EMF) induced by motion relative to a magnetic field B.
    • An electromotive force (EMF) induced by motion relative to a magnetic field B is called a motional EMF.
    • In the case where a conductor loop is moving into magnet shown in (a), magnetic force on a moving charge in the loop is given by $evB$ (Lorentz force, e: electron charge).
    • Equating the two forces, we get $E = vB$.
    • Formulate two views that are applied to calculate the electromotive force

  • Another velocity-dependent force: the Zeeman effect

    • Remember, the restoring force is just a linear approximation to the Coulomb force and therefore , the "spring constant'', is the first derivative of the Coulomb force evaluated at the equilibrium radius of the electron.
    • Now let's suppose we apply a force that is not spherically symmetric.
    • This results in another force on the electrons of the form $q \dot{\mathbf{r}} \times B\hat{\mathbf{z}}$ (from Lorentz's force law).
    • Adding this force to the harmonic ( $-k \mathbf{r}$ ) force gives
    • Zeeman was a student of the great physicists Onnes and Lorentz in Leyden.

  • Tensors

    • Let's use the Lorentz matrix to transform to a new frame
    • This just means a Lorentz invariant number at each point and time.
    • Let's look first at the Lorentz force equation,

  • Phase-Space Density

    • where ${\bf F}$ is a force that accelerates the particles.
    • We would like to define some quantities that are integrals over momentum space that transform simply under Lorentz transformations.