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# Thomson's Apparatus

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A diagram for the Thomson's apparatus is given in the attachment. (a) Show that the total deflection of the beam is given by y1 + y2 = e/m*[(B^2)/E][(x1^2)/2 + x1*x2] where B is the magnetic field and E the electric field. (b) Show that the angle the electron is deflected is given by theta = e/m * [Ex1/(u^2)].

##### Solution Summary

Figure 1: The forces acting on the electrons in Thomson's experiment
Let
l be the length of the plates
E be the electrostatic field
B be the magnetic field
q the charge on one electron
m the mass of one electron
u the velocity in the x-direction (this remains constant)
Then when only the electric field is present the electrostatic force in the y-direction is: F = qE.
The acceleration in the y-direction is: a = F/m so a = qE/m

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