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^rightarrow 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 straight line. The balancing condition provides a relationship involving the velocity v^rightarrow of the particle. In this problem you will figure out how to arrange the fields to create this balance and then determine this relationship. 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. (Figure 2) Express the magnetic field B_bal that will just balance the applied electric field in terms of some or all of the variables q, v, and E.

Explanation / Answer

B)
Electric force = Magnetic force
qE = Bqv
E and B are electric and magnetic fields, v is the velocity and q is the charge.
Cancelling q on both the sides,
E = Bv
B = E/v

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