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## Section 4.4: Exploring the e/m Experiment

Electric field = kV / m

Please wait for the animation to completely load.

The animation illustrates the deflection of an electron in external fields which simulates J. J. Thomson's experiment with cathode rays (position is given in mm, 10−3 m). Restart.  You can change the value of the electric field and play it with the magnetic field, of 2 mT, on or off. After determining that a cathode ray beam was negatively charged, Thomson performed several experiments to further determine the properties of these cathode ray beams, made up of what we now call electrons. By knowing the value of the force on the particles and their initial speed, he reasoned he could determine the mass/charge of the particles.

First, Thomson determined the speed of the rays in the cathode ray tube by passing the beam through crossed electric and magnetic fields. The force on a charged particle with charge q is given by the Lorentz force, F = −q (E + v × B) , where v is the velocity of the charge, and E and B are the electric and magnetic fields, respectively. In this animation, when the magnetic field is off, the particle deflects upward because of the electric field created by the charges shown on the plates ("+" and "−" charges on the blue and green plates).  Given a velocity to the right, in what direction should the magnetic field be to deflect the particles downward?  Once the magnetic field is on, if the electric field is set correctly, the beam does not deflect. Try different values of the electric field until there is no longer a deflection. From this, determine the velocity of the particle. Note that the analysis was all done non-relativistically. Is the speed slow enough to justify this?

Once you have calculated the velocity, turn off the magnetic field and measure the deflection of the beam. Measure the distance the particle deflects in the electric field (the y distance from its entry into the field to its exit). The force is given by F = qE so the acceleration in the vertical direction is qE/m and the acceleration in the horizontal direction is zero. Therefore, from basic mechanics,

y = 1/2 (qE/m) t2     and     x = vt,

and since you cannot measure the time in the animation (just as Thomson could not measure the time the electron was in the field), combine the two equations to solve for the deflection of y for electrons traversing a distance x and determine the value of q/m, here e/m. There is not any way, in this experiment, to get a value for the mass or the charge independently. Why?