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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)].

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    https://brainmass.com/physics/electricity-magnetism/thomson-s-apparatus-18361

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    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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