In 1897, English physicist J.J. Thomson "discovered" the electron with a very elegant and relatively simple experiment. Consider shooting a beam of electrons at a constant speed through a region of uniform electric and magnetic fields and , respectively. The directions of , and are all perpendicular to one another.

a) What direction(s) should the two fields point in so that the two forces on the electrons (magnetic and electric) counteract one another? b) Imagine the scenario in which the and fields have been tuned so that the net force on the electrons is zero. What is the speed of the electrons? c) If you now turn off the electric field, what happens to the particles? What is the charge-to-mass ratio (/) of an electron (in terms of the above variables)?