help please In the figure below a charged particle (either an electron or proton
ID: 2119540 • Letter: H
Question
help please
In the figure below a charged particle (either an electron or proton) with an initial kinetic energy K0 enters region 1 at time t = 0. That region contains a uniform magnetic field directed into the page, with magnitude B1. The particle goes through a half-circle and then exits region 1, headed toward region 2 across a gap of length d. There is an electric potential difference Delta V across the gap with a polarity such that the particle's speed increases uniformly as it traverses the gap. Region 2 contains a uniform magnetic field directed out of the page with magnitude B2. The particle goes through a half-circle and then leaves region 2. Our goal in this problem is to determine the amount of time the particle spends in region 1, in the gap between the two regions, and in region 2. Is the charged particle an electron or proton? Explain. Determine the amount of time the particle spends in region 1. Put your answer in terms of B1, B2, K0, Delta V, d, and physical constants (e.g. elementary charge, proton mass, electron mass, etc.). Determine kinetic energy of the particle after it moves through the gap. Put your answer in terms of B1, B2, K0, Delta V, d, and physical constants. Determine the amount of time the particle spends in the gap between the two regions. Put your answer in terms of B1, B2, K0, Kf, Delta V, d, and physical constants Determine the amount of time the particle spends in region 2. Put your answer in terms of B1, B2, K0, Kf, Delta V, d, and physical constants.Explanation / Answer
a) an electron --- as it is moving clockwise in downwad MF ..
b) w= eB1/m where e is elcetron charge and m-- electron mass ... so t = pi/w = pi*m/eB1 [as pi radian is revolved by the elctron]
c) final KE = Ko + e(deltaV)d [using energy conservation]
d) d= ut + .5a*t^2 => t= [-u + sqrt(u^2 + 2ad)]/a .... where a =e*deltaV/md and u =sqrt(2Ko/m)
e) usin same reasoning as b) we get t= pi*e/eB2
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