# 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

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