When a charged particle enters in a uniform magnetic field, its kinetic energy

Concept –

Motion of the charged particle in a uniform magnetic field –

When a charge particle q enters a magnetic field \(\vec B\) with a velocity \(\vec v\), it experiences a force

\(\vec F = q\left( {\vec v \times \vec B} \right)\)

The direction of this force is perpendicular to both \(\vec v\) and \(\vec B\). The magnitude of this force is

F = qvB sin θ

Explanation –

The direction of this force is perpendicular to both \(\vec v\) and \(\vec B\) and the magnitude of this force is given as

F = qvB sin θ

If a charge particle enters a magnetic field with velocity v such that the direction between the velocity of the charge particle q and magnetic field B is 90°, then it experiences a maximum force.

Here θ = 90°, so

F = qvB sin 90° = qvB = a maximum force

As the magnetic force acts on a particle perpendicular to its velocity, it does not do any work on the particle. It does not change the kinetic energy or the speed of particle.

The magnetic field B is perpendicular to the paper and going into it (show by small cross). A charge +q is projected with speed v in the plane of the paper. The velocity is perpendicular to the magnetic field. A force F = qvB acts on the particle perpendicular to both \(\vec v\) and \(\vec B\). This force continuously deflects the particle sideways without changing its speed and particle will move along a circle perpendicular to the field.