14. Acceleration in a cyclotron. Suppose in a cyclotron that B = 2B and E, = E cos w t E, = - E sin wet 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 we. Show that the displacement of a particle is described by x(t) = qE Mw2 (wet sin wat + cos wet - 1) qE Mw 2(wet cos wet- sin wat) Mw² where at t=0 the particle is at rest at the origin. Sketch the first few cycles of the displacement.
14. Acceleration in a cyclotron. Suppose in a cyclotron that B = 2B and E, = E cos w t E, = - E sin wet 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 we. Show that the displacement of a particle is described by x(t) = qE Mw2 (wet sin wat + cos wet - 1) qE Mw 2(wet cos wet- sin wat) Mw² 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:14. Acceleration in a cyclotron. Suppose in a cyclotron that
B = 2B and
E₂ = E cos w t
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 we. Show
that the displacement of a particle is described by
x(t) =
qE
Mw, 2
Ey
qE
Mw ²
= - E sin wet E = 0
(wet sin wet + cos wet - 1)
y(t)
where at t = 0 the particle is at rest at the origin. Sketch the
first few cycles of the displacement.
(wet cos wet sin wet)
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