# Force on a moving charge in a magnetic field – formula

Last updated on April 6th, 2023 at 01:58 pm

When a charged particle (or charge) moves in a magnetic field, a magnetic force acts upon it. In this post, we will discuss this and obtain the **formula of the Force on a moving charge or a charged particle in the magnetic field**. This force is the magnetic component of the well-known Lorentz force on a moving charge.

## Force on a moving charge in a magnetic field & its formula

Let the charge on the particle is q. And, say that the charged particle is moving with velocity v in the magnetic field. Let the magnetic field is B. And, the angle between v and B be θ.

The force on the moving charge in a magnetic field is expressed by the following formula.

F = qvB sin θ

In vector form,

Force on a moving charge in magnetic field – formulaF= q (vxB)

The direction of this force can be determined by using **Fleming’s Left Hand Law**.

[ Also read: Force on a current-carrying conductor in a magnetic field]

## The maximum value of the force on a moving charge in a magnetic field

When the charge moves perpendicular to the direction of the magnetic field, i.e. the angle between v and B is 90 degrees, then the force on the charge becomes maximum, and then the force becomes F_{max} = qvB

## The minimum value of the force on a moving charge in a magnetic field

When the charge moves parallel to the direction of the magnetic field, i.e. the angle between v and B is 0 degree, then the force on the charge becomes minimum, and then the force becomes F_{min} = 0.

[ Related: Force on a current-carrying conductor in a magnetic field]