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mmainak
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Homework Statement
Electrons emitted with negligible speed from an electron gun are accelerated through a potential difference v along the X-axis. These electrons emerge from a narrow hole into a uniform magnetic field B directed along this axis. However, some of the electrons emerging from the hole make slightly divergent angles as shown in figure. Show that these paraxial electrons are refocused on the X-axis at a distance
sqrt:(8.pi^2.m.V/e.B^2).
Homework Equations
The Attempt at a Solution
m.w^2.r =B.e.V
w= B.e/m ... cyclotron frequency
T= 2.pi.m/B.e
e.V/m = f(acc).d => f= e.V/m.d
d= 1/2.f.T^2 = 1/2. e.V/m.d . 4.pi^2.m^2/B^2.e^2
=> d=sqrt:(2.pi^2.m.V/B^2.e)
2 should be 8 in the actual answer.
Where did I go wrong?
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