Force on a moving charge in a magnetic field – formula

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, F = q (v x B)

Force on a moving charge in magnetic field – formula

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 Fmax = 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 Fmin = 0.

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

Force on a moving charge in a magnetic field – formula
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