For PS#45, how do I know that C is better than A? I recognized that C was true, but I figured if you are shooting a particle into these machines, then you'd probably know what particle you're shooting. That, and I thought identifying what particle you're shooting was too far from the main purpose of the passage.
I honestly had the worst luck with this passage and had to guess on a couple but this was one I should have gotten because I knew what they were going for. The machines are analyzing intrinsic properties of the particle in question. More time to analyze the sample isn't something of a concern for them (I'm guessing that it's because everything happens so fast in general that time isn't a constraint they can really vary) because it doesn't help as much in defining the particle as, say, curving the trajectory.
Think about it this way
A charge moving through a magnetic field is pushed by a force (F), which causes the particle to curve either in one or the other direction based upon the direction of the current. This Force is the same force we find out using the right hand rule and can actually be considered a centripetal force on the object. Thus: F = Mv^2/r = qvB. From this, we can see how the radius of curvature is an excellent way of figuring out the particle because each particle will have a differing radius of curvature based upon each particles properties (charge, mass, etc).
One final thing; although time MAY be helpful, the question still asks which is the best. I hate these questions as much as the next person, but the question specifically asks for the curvature and if you remember that above equation it can help a lot in understanding that. Not to mention, it helps you see that the force doesn't do any work on the particle in question, but is instead a centripetal force in a magnetic field.
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Sorry for that, I completely mistook your question. Let me answer your REAL question. The passage states that these accelerators are used to examine the properties of the particles emerging from the collisions, thus, they do not know what the particles are. Thus, using something like radius of curvature in the above would help in determining the charge and mass of particles, which would help in saying what each particle is. And you're not "shooting" a particle, the particle is accelerated from a collision. You're measuring the after effects of the collision. So the particle may be known beforehand, but the aim is to determine what comes out of the collision.
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What the hell; I thought cathodes attracted electrons? Why does it say that the electrons are accelerated to the anode?