The right-hand rule

The Lorentz force.

Introductory remarks

Schoolchildren usually use the right-hand rule to determine the deflection direction of a charged particle, moving in a magnetic field.

The force that deflects such particles is called the Lorentz force

The magnitude of the Lorentz force is calculated at school with the formula

F = q ⋅ v ⨯ B

B – the magnetic induction vector

v – the velocity of the particle

q – the charge of the particle

⨯ – this is the vector product.

After multiplying the charge by the velocity and the induction we get the Lorentz force. Its magnitude can be calculated on a calculator by simply multiplying the remaining quantities by each other.

Any force is a vector, so a force has not only a magnitude but also a direction.

The direction of any vector product is easy to find if you know the directions of the factors.

That is what the right-hand rule.

And as you may have guessed, it can be applied not only to the Lorentz force but to any other vector products.

Required knowledge

Before getting to know the right-hand rule you have to learn how the direction of electric current is defined.

Electrons and negatively charged ions move from the cathode to the anode.

Protons, holes and positively charged ions move in the opposite direction, from the anode to the cathode.

The direction of electric current is taken to be the direction opposite to the one in which electrons move.

The right-hand rule is shown as follows:

The direction in which a particle is deflected from its original trajectory by a magnetic field depends on the charge of the particle.

The direction of the Lorentz force

The direction of the Lorentz force is shown by the brown arrow. The force itself is labelled F. Blue shows the trajectory of negatively charged particles provided that:

• the negatively charged particle initially flew from left to right
• the magnetic field induction vector points out of the screen

Red shows the trajectory of a positively charged particle under the same conditions.

The straight black line shows the motion of a particle that has no charge. The magnetic field does not act on it and it keeps moving from left to right.

Article author: Andrei Olegovich