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

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Unformatted text preview: Physics 2212 Quiz #1 Solutions Fall 2009 Permittivity constant m p Mass of a proton 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 , 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 are able to leave the capacitor through a small hole in its lower plate at distance from the left capacitor edge. What is v ? 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 + v x ( t ) + 1 2 a x ( t ) 2 where x = , x = 0, v x = v , and a x = 0, so = v ( t ) t = v In the vertical ( y ) direction: y = y + v y ( t ) + 1 2 a y ( t ) 2 where y = d/ 2, y = 0, v 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,...
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Quiz1Solution - Physics 2212 Quiz #1 Solutions Fall 2009...

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