E = -720j N/C x _Target – R- Proton beam E = 0 below the plane Figure P22.26 Using the identity sin 20 = 2 sin 0 cos 0 (see Appendix B.4), we can write R in the more compact form v? sin 20, R = (4.20) g
Protons are projected with an initial speed υi = 9.55 km/s from a field-free region through a plane and into a region where a uniform electric field E→ = 2720ĵ ⁄ NyC is present above the plane as shown. The initial velocity vector of the protons makes an angle θ with the plane. The protons are to hit a target that lies at a horizontal 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 vertical motion of the protons above the plane? (c) Argue that Equation 4.20 would be applicable to the protons in this situation. (d) Use Equation 4.20 to write an expression for R in terms of υi , 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 the figure for each of the two possible values of θ.
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