Lorentz Force

Hendrik Antoon Lorentz was a Dutch physicist who explained the theories related to electromagnetic radiation. He mainly concentrated on the relationship between magnetism, light, and electricity.

What is Lorentz Force?

Lorentz force is defined as the combination of the magnetic and electric force on a point charge due to electromagnetic fields. It is used in electromagnetism and is also known as the electromagnetic force. In the year 1895, Hendrik Lorentz derived the modern formula of Lorentz force.

What is Lorentz Force Formula?

Lorentz force formula for the charged particle is as follows:



  • F is the force acting on the particle
  • q is the electric charge of the particle
  • v is the velocity
  • E is the external electric field
  • B is the magnetic field

Lorentz force formula for continuous charge distribution is as follows:



  • dF is a force on a small piece of the charge
  • dq is the charge of a small piece

When a small piece of charge distribution is divided by the volume dV, the following is the formula:

f = \(\rho\) (E+v*B)


  • f is the force per unit volume
  • ⍴ is the charge density

With the help of the right-hand rule, it becomes easy to find the direction of the magnetic part of the force.

What is the importance of Lorentz force?

Lorentz force explains the mathematical equations along with the physical importance of forces acting on the charged particles that are traveling through the space containing electric as well as the magnetic field. This is the importance of the Lorentz force.

Right-Hand Rule

The right-hand rule is useful to find the magnetic force as it becomes easy to visualize the direction as given in Lorentz force law.

Right hand rule

From the above figure, it is understood that the magnetic force is perpendicular to both the magnetic field and charge velocity.

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Applications of Lorentz Force

The following are the applications of Lorentz force:

  • Cyclotrons and other particle accelerators use Lorentz force.
  • A bubble chamber uses Lorentz force to produce the graph for getting the trajectories of charged particles.
  • Cathode ray tube televisions use the concept of Lorentz force to deviate the electrons in a straight line so land on specific spots on the screen.

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