# Magnetic Force Formula

## Magnetic Force Formula

Magnetic force is the force of attraction or repulsion that arises between electrically charged particles due to their motion. It is the basic force responsible for effects like action of electric motors or attraction of iron pieces towards magnet.

In other words, magnetic force is the force experienced because of the magnetic field. It can be positive or negative depending whether the force is attractive or repulsive.

Magnetic force is based on the charge, velocity and magnetic field of the object.

The magnetic force formula is given by,

$F_{B}=qv\times&space;B$

$F_{B}=qvBsin\theta$

Wherein,

FB = magnetic force,

q = charge,

v = velocity,

B = magnetic field and

Î¸ = angle between the track of the second particle and direction of magnetic field.

Example1

Determine the magnetic force of a 5C charged particle moving with a velocity of 10m/s in a magnetic field of 1T. The direction of magnetic field is perpendicular to the track of the second particle.

Solution:

Given parameters are,

q = 5C,

v = 10m/s,

B = 1T

Since the path of second particle is perpendicular magnetic field direction,

Î¸ = 90Â°

The magnetic force formula is given by,

FB = q v B sinÎ¸

FBFB = 5 Ã— 10 Ã— 1 Ã— sin 90

Â Â Â Â  = 50N

Example 2

Determine the magnetic force of 50C charged particle moving with a velocity of 3m/s in an magnetic field of 1T? The direction of magnetic field is same as path of the second particle.

Solution:

Given parameters are,

q = 50C,

v = 3m/s,

B = 1T

Since the path of second particle is same as magnetic field direction,

Î¸ = 0Â°

The magnetic force formula is given by

FB = q v B sinÎ¸

= 50 Ã— 3 Ã—1 Ã— sin 0

=0