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distance d: 48. GP Protons are projected with an initial speed v;- rom a field-free region through a plane and into 0j N/C is /s f a region where a uniform electric field E 72
present above the plane as shown in Figure P23.48. The initial velocity vector of the protons makes an angle 0 with the plane. The protons are to hit a target that lies at a hori- zontal distance of R- 1.27 mm from the point where the protons cross the plane and enter the electric field. We wish to find the angle θ at which the protons must pass through the plane to strike the target. (a) What analysis model describes the horizontal motion of the protons above the plane? (b) What analysis model describes the ver- 52 tical motion of the protons above the plane? (c) Argue that Equation 4.13 would be applicable to the protons in this situation. (d) Use Equation 4.13 to write an expression for Rin terms of v, E, the charge and mass of the proton, and the angle θ. (e) Find the two possible values of the angle θ. (f) Find the time interval during which the proton is above the plane in Figure P23.48 for each of the two possible val- ues of 8 53. Ε--72oj N/C x Target 54. A Proton beam E 0 below the plane 55. Figure P23 48
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