Q. 535.0( 2 Votes )

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.

Answer :

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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