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# DQ2D_solution - When the beam enters the device its...

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Discussion Question 2D P212, Week 2 An Electrostatic Quadrupole The figure below shows a head-on view of four long, parallel charged rails (they extend both into and out of the page). The side rails carry a positive charge per unit length + λ . The top and bottom rails have the same charge density, but with opposite sign (i.e. they are negatively charged). This arrangement forms an electrostatic quadrupole . In the questions below, you will discover why it is useful in devices which contain beams of moving charged particles. We will not perform any calculations in this question … all you need is your physical intution. (a) Sketch the electric field lines in the interior region of the quadrupole. Lines go from positive to negative poles. (b) Given your sketch, where is the electric field the strongest ? Where is it the weakest ? Strongest at any pole, weakest at center. (c) Now imagine that a beam of moving electrons enters the quadrupole, with velocity parallel to the charged rods.
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Unformatted text preview: When the beam enters the device, its cross-sectional profile is circular. What will the beam look like when it exits the quadrupole on the other side? (Assume that the force exerted on the electrons is not too large.) The beam of electrons would be flattened into a oval that is long in the x-axis and short in the y-axis. (d) The cathode ray tube (CRT) in a TV monitor contains a beam of electrons directed towards a fluorescent screen. The screen lights up where the beam hits it. If you were an electrical engineer designing such a CRT, why might you find it useful to pass the electron beam through a quadrupole before it hits the screen? (A little hint: quadrupoles are usually used in pairs … can you figure out why?) The quadrupole acts to correct errors in the electron firing gun. Non-perfect electrons will still hit pixel. x y + λ +--beam of electrons heading into page y x + +--rods extend into and out of page d d...
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