Magnetic force on charged particles

Whenever a charged particle travels through a magnetic field, it will experience a force by the magnetic field. This magnetic force is sometimes referred to as the Lorentz force. The magnitude of this force can be evaluated by the following equation:

It is important to note that only the component of velocity which is perpendicular to the magnetic field is used in the equation. If the charged particle is moving parallel to the magnetic field, then it would not experience any force because it doesn’t have perpendicular component to the magnetic field. However, if the same charged particle was travelling exactly perpendicular to the magnetic field, then it would experience the maximum force. The diagram below shows this visually:

*diagram*

Direction of the force

The equation above is only useful to determine the magnitude of the force, not the direction. To determine the direction of this force on the charged particle, we use the right hand palm rule. The rule is as follows:

• Take your right hand and ensure your fingers are stretched out and flat

• Point your thumb in the direction that the charged particle is moving

• Rotate your hand so that your fingers point in the direction of the magnetic field (i.e. where the arrow is pointing)

• The direction that your palm is facing is the direction of the force that a positive charged particle will experience

Notice that the above rule gives the direction for a positive charged particle. If it is a negative charged particle, then the direction of the force is simply the opposite direction (i.e. the opposite direction to where your palm is facing). Whenever using this rule, make sure to double check if the charged particle is positive or negative and remember that the direction your palm is facing would be the direction of force that a positive charged particle would experience, and opposite direction for a negative charged particle.