Question

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 E⃗  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 v⃗  of the particle. In this problem you will figure out how to arrange the fields to create this balance and then determine this relationship. Figure 1 of 2The ion source on the left and two horizontal plates spaced a distance d apart on the right are shown in xy plane. The upper plate has a 0 potential, and the lower plate has a potential equal to the product module E by module d. The vertical screen with a slit in its center is placed to the right from the plates. The x-axis points to the right, and the y-axis points upward. $V 0 on Ions out source d slit V = |E\\a$ 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 Bbal that will just balance the applied electric field in terms of some or all of the variables q, v, and E.

Answer 1

Bbal = E/v

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