Question 3: What is the magnitude of the force on a charge q moving with a velocity v in a magnetic field B?

## Force on a charged particle in a magnetic field

When a charged particle is brought in the electric field due to some other charge, it experiences a force whose direction depends upon the sign of the charge. Similarly, a charged particle also experiences a force when in the magnetic field. However, the condition is the charged particle must be moving in the magnetic field. This is because the force on the moving charged particle is due to the interaction of the magnetic fields produced by the moving charge and the external magnetic field in which it is moving.

## Magnitude calculation of the force

If a positive charge q is moving with a velocity v in a magnetic field B, then the experimentally found value of the force on the charged particle is given by

Here θ is the angle between velocity v of the charged particle and B, the external magnetic field.

#### Special cases for magnitude calculation of the force

Since for a given value of q, v and B, the magnitude of force depends upon the angle θ between v and B, therefore, the force will be maximum if this angle is 90° (because sin90°is maximum) and will be 0 (or minimum) if the angle between v and B is 0° (because sin 0° is zero).

Mathematically