Electromagnetic Velocity Filter When a particle with charge q moves across a mag

Question

Electromagnetic Velocity Filter When a particle with charge q moves across a magnetic field of magnitude B. it experiences a force to the side. If the proper electric field E is simultaneously applied, the electric force on the charge will be in such a direction as to cancel the magnetic force with the result that the particle will travel in a strait line. The balancing condition provides a relationship involving the velocity v of the particle. In this problem you will figure out how to arrange the fields to create this balance and then determine this relationship. Part A Consider the arrangement of ion source and electric field plates shown m the figure. The ion source sends particles with velocity v along the positive x axis. They encounter electric field plates spaced a distance d apart that generate a uniform electric field of magnitude E in the +y direction. To cancel the resulting electric force with a magnetic force, a magnetic field (not shown) must be added in which direction? Using the right-hand rule, you can see that the positive z axis is directed out of the screen. Choose the direction of B. Part B Now find the magnitude of the magnetic field that will cause the charge to travel in a straight line under the combined action of electric and magnetic fields.

Explanation / Answer

For the charge to move straight, net force has to be zero

So, magnetic force = electric force

So, qvB = (V/d)*q <------- Electric force = E*q = (V/d)*q

So, B = V/d*v

Now, V = E*d

So, B = E*d/(dv) = E/v <---------answer (does not depend on q)

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