Acceleration in a cyclotron. Suppose in a cyclotron that B = 2B and E₂ = E cos w t E = - E sin wat E₂ = 0 with E constant. (In an actual cyclotron the electric field is not uniform in space.) We see that the electric field intensity vector sweeps around a circle with angular frequency . Show that the displacement of a particle is described by x(t) = y(t) = qE Mw² 2(wt sin wat + cos wat - 1) 9E Mw2 z(wt cos wt - sin wat) where at t = 0 the particle is at rest at the origin. Sketch the first few cycles of the displacement.
Acceleration in a cyclotron. Suppose in a cyclotron that B = 2B and E₂ = E cos w t E = - E sin wat E₂ = 0 with E constant. (In an actual cyclotron the electric field is not uniform in space.) We see that the electric field intensity vector sweeps around a circle with angular frequency . Show that the displacement of a particle is described by x(t) = y(t) = qE Mw² 2(wt sin wat + cos wat - 1) 9E Mw2 z(wt cos wt - sin wat) where at t = 0 the particle is at rest at the origin. Sketch the first few cycles of the displacement.
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Transcribed Image Text:Acceleration in a cyclotron. Suppose in a cyclotron that
B = 2B and
E₂ = E cos w t E = - E sin w t
E = 0
with E constant. (In an actual cyclotron the electric field is
not uniform in space.) We see that the electric field intensity
vector sweeps around a circle with angular frequency w.. Show
that the displacement of a particle is described by
x(t) =
y(t) =
qE
Mw 2
qE
Mw2
(wet sin wet + cos wet- 1)
(wet cos wet sin wet)
where at t = 0) the particle is at rest at the origin. Sketch the
first few cycles of the displacement.
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