Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of velocity or energy of the particle.
When a charged particle with charge q moves inside a magnetic field `vecB`with velocity v, it experiences a force, which is given by:
Here, `vecv` is perpendicular to `vecB`,`vecF`is the force on the charged particle which acts as the centripetal force and makes it move along a circular path.
Let m be the mass of the charged particle and r be the radius of the circular path.
v and B are at right angles:
Time period of circular motion of the charged particle can be calculated as shown below:
∴ Angular frequency is
Therefore, the frequency of the revolution of the charged particle is independent of the velocity or the energy of the particle.