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Quiz1Solution - Physics 2212 Fall 2009 Quiz#1 Solutions...

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Physics 2212 Quiz #1 Solutions Fall 2009 ² 0 Permittivity constant m p Mass of a proton μ 0 Permeability constant m e Mass of an electron e Fundamental charge c Speed of light K Coulomb constant g Acceleration due to gravity Unless otherwise directed, friction, drag, and gravity should be neglected, and all batteries and wires are ideal. Any integrals in free-response problems must be evaluated. I . (16 points) The parallel plate capacitor (surface charge density η , side length L , distance d between the plates; where L d ) shown below acts as a “velocity filter” for a beam of electrons that enters the capacitor from the left centered between its plates, and moving initially straight to the right. That is, only electrons entering with a certain speed v 0 are able to leave the capacitor through a small hole in its lower plate at distance from the left capacitor edge. What is v 0 ? Express your answer in terms of parameters defined in the problem and physical or mathematical constants. . . . . . . . . . . . . There is no horizontal force on the electron, so its horizon- tal acceleration is zero. Because the electric field between parallel plates with L d is uniform, there is a constant vertical force on the electron, ~ F = q ~ E , so the vertical accel- eration is constant. This is essentially a projectile motion problem. Choose a coordinate system, and then use con- stant acceleration kinematics in the horizontal and vertical directions, linked by time. Find the time for the electron to reach the hole from the horizontal ( x ) information: x = x 0 + v 0 x t ) + 1 2 a x t ) 2 where x = , x 0 = 0, v 0 x = v 0 , and a x = 0, so = v 0 t ) Δ t = v 0 In the vertical ( y ) direction: y = y 0 + v 0 y t ) + 1 2 a y t ) 2 where y = d/ 2, y 0 = 0, v 0 y = 0, and (in terms of magnitudes) a y = F y /m = qE/m = eE/m e . Recall that the electric field between two parallel plates is related to the area charge density on the plates, E = η/² 0 .
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