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.
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.
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.