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ELECTROSTATIC DEFLECTION 1 1
ELECTROSTATIC DEFLECTION OF THE
PARTICLE.
Let us suppose as before that the particle is projected with
a velocity v parallel to the axis <Ax: let the electric force act- ing on the particle be parallel to the axis of z and equal to Z, then the equation of motion of the particle under the electric force is |
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(z «z
When the deflection is small, — =#2 __ approximately,
£t&" €&%?*
and hence
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or z =
= ^B
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where B
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= f
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thus B is quite independent of the charge, mass, or velocity of the
particle, and depends merely on the distribution of the electric field and the distance from the point of projection at which the deflection is measured.
A very convenient method of producing the electric field is
to have two parallel plates perpendicular to the axis of z ; in this case the electric field is approximately constant between the plates and vanishes outside them. If b is the length of the plates measured parallel to the axis of x, and if one end of the plates just comes up to the point from which the particle is projected, putting Z==Z from x=*o to #=#, and Z=*o from
*= b to *=/, we find that B= Z£ ( / - ^\
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