A device called a velocity selector allows particles of a specific velocity pass

Question

A device called a velocity selector allows particles of a specific velocity pass through a specified region undetected. First, show that v= E/B if the electric field is directed perpendicularly to a magnetic field. Then show why the sign of charge does not matter.

Explanation / Answer

the force due to magnetic field is given by Fb = q*v*B and the force due to electric field is given by Fe = q*E now for the particle to pass undeflected the two forces should be equal => Fb = Fe => E = v*B now if the sign of the charge of the particle changes the electric force and the magnetic force both change their sign and hence the particle passes even then since the charge is involved in the expression for the two forces.

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