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, following is the formula:

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


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

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

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