is charge to mass ratio the normal EMF that we observe into the circuits and how it is directly proportional to the displacement or amount of deflection for given velocity????

Solution
First part of your question is not clear.
I am answering second part of the question.

Thomson observed that the particles of the cathode deviate from their path. He noticed the amount of deviation in the presence of electrical or magnetic field depends on various related parameters. They are:

1. Particles with a greater magnitude of the charge experienced greater interaction with the electric or magnetic field. Thus, they exhibited a greater deflection.
2. Lighter particle experienced greater deflection. Thus, deflection is inversely proportional to the mass of the particle.
3. Deflection of the particle from their path is directly proportional to the strength of the electrical and the magnetic field present.

The angle of deflection of charged particle in an electric field is directly proportionate to the charge / mass ratio.

The greater the charge and smaller the mass, the greater the extent of deflection.


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