Consider the situation of the previous problem. A particle having charge q and mass m is projected from the point Q in a direction going into the plane of the diagram. It is found to describe a circle of radius r between the two plates. Find the speed of the charged particle.
Given:
Charge of the particle = q
Mass of the particle = m
Radius of circle described by the particle between the two plates = r
Formula used:
Ampere’s circuital law states that the line integral of the magnetic field for a closed surface is μ0 times the current enclosed by the surface.
where B = magnetic field, dl = line element, μ0 = magnetic permeability of vacuum, I = current enclosed.
Now, from the previous problem, we found out that the magnetic field(B) at point Q is μ0K, where μ0 = magnetic permeability of vacuum, K = surface current.
Also, we know that the velocity of a particle in a magnetic field is given as
Where
q = charge of particle, B = magnetic field, r = radius of circle described by particle, m = mass of particle.
Substituting the value of B, we get
Velocity of the particle is