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DQ7B_solution - Discussion Question 7B P212 Week 7 Lorentz...

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Discussion Question 7B P212, Week 7 Lorentz Force on Moving Charges The figure below depicts a region of space (shaded) where there is a constant magnetic field, B = 1.2 T, directed along the negative z axis (into the page). The magnetic field region extends infinitely far in the positive and negative y directions, but is constrained to the region between x = 0 and x = 1 m. A proton travels along the x axis toward this region, with initial speed v 0 . (a) What is the radius of curvature of the proton's path after it enters the magnetic field region? To describe the particle's circular path, match the Lorentz force exerted by the B field to the centripetal force. 2 Using The Lorentz force provides the centripetal force to allow the proton to accelerate ab in a direction perpendicular to the prot out on a ci velocity: F F 1 F rcle F ma qv B qvB v mv qvB ma m r r qB = = × = = = = = = r r r ( )( ) ( )( ) .67 27 kg 2 8 / 1.74 m 1.6e-19 C 1.2 e e m s = Τ (b) At what x and y positions will the proton leave the magnetic field region?
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