Lorentz force: The movement of charged particles in a magnetic field

The Lorentz force describes the force that acts on an electrically charged particle or a current conductor when they are in a magnetic field. It is a central concept in electrodynamics and was named after the Dutch physicist Hendrik Antoon Lorentz (1853-1928). The Lorentz force is responsible for many fundamental phenomena in physics and technology, such as the function of electric motors and particle accelerators.

Formula of the Lorentz force

The Lorentz force ? on a charged particle with the charge q, which moves with the speed ? in a magnetic field ?, is described by the following formula:

? = q - (? × ?)

Where:

• ? The Lorentz force (in newtons, N)
• q: The electric charge (in coulombs, C)
• ? The speed of the particle (in metres per second, m/s)
• ? The magnetic flux density (in Tesla, T)

The symbol "×" stands for the cross product, which indicates the direction of the force. The direction of the Lorentz force is perpendicular to both the movement (?) of the particle and the magnetic field (?). It can be determined using the right-hand rule.

Properties of the Lorentz force

• Directional dependence: The force always acts perpendicular to the movement and the magnetic field, which often leads to a circular or spiral path of the particle.
• Speed dependence: The faster the particle moves, the stronger the Lorentz force.
• No work: The Lorentz force does no work on the particle, as it always acts perpendicular to the direction of movement. It therefore only changes the direction, but not the speed.

Applications of the Lorentz force

The Lorentz force has numerous applications in science and technology:

• Electric motors: Current-carrying conductors in magnetic fields experience movement due to the Lorentz force, which forms the basis for the operation of electric motors.
• Particle accelerators: Charged particles are kept on circular paths by the Lorentz force, as in the Large Hadron Collider (LHC).
• Magnetic field sensors: Devices such as Hall sensors measure the Lorentz force to determine the strength of magnetic fields.
• Plasma physics: In fusion reactors such as tokamaks, the Lorentz force helps to control and confine the hot plasma.

Interesting facts about the Lorentz force

Did you know that the Lorentz force is used in magnetohydrodynamic drives, such as those tested in some modern ships? Here, water is ionised and accelerated by the Lorentz force, which enables almost silent locomotion.