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.
it may seem strange that the selected velocity does not depend on either the mass or the charge of the particle. (for example, would the velocity of a neutral particle be selected by passage through this device? ) the explanation of this is that the mass and the charge control the resolution of the device--particles with the wrong velocity will be accelerated away from the straight line and will not pass through the exit slit. if the acceleration depends strongly on the velocity, then particles with just slightly wrong velocities will feel a substantial transverse acceleration and will not exit the selector. because the acceleration depends on the mass and charge, these influence the sharpness (resolution) of the transmitted particles.
assume that you want a velocity selector that will allow particles of velocity v⃗ to pass straight through without deflection while also providing the best possible velocity resolution. you set the electric and magnetic fields to select the velocity v⃗ . to obtain the best possible velocity resolution (the narrowest distribution of velocities of the transmitted particles) you would want to use particles with
assume that the selector is short enough so that particles that move away from the axis do not have time to come back to it.
assume that the selector is short enough so that particles that move away from the axis do not have time to come back to it.
a. both q and m large
b. q large and m small
c. q small and m large
d. both q and m small
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