problem-solving guide(1)

For the first problem on the second midterm if you

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Unformatted text preview: and that the energy at infinity is zero no matter what direction you approach infinity, then you automatically knew the answer to the second half of the problem was the same as the answer to the first. Seeing the “trick” is difficult, but really it’s the essence of doing physics: symmetry, conservation of energy, and approximations are what allow us to reduce physics problems to things we can understand. Symmetry plays an enormous role in this course especially, since we do all those integrals using Gauss’s and Ampère’s law, which require the distributions of charge and current to be symmetric. In fact, the reason physics is so math- intensive is that the math we use was developed precisely to explain the physics. What this means is the math isn't fundamental; the physics is. Math is the language we use to express that physics, and you have to understand the physics or the math you use will go nowhere. This is why you can’t just write down the equations with the same letters as given in the problem and expect to get the answer. Given all this, you should include in your formula sheet the guiding principles of the class. Symmetry is one; conservation of energy is another. I’d have to think to come up with a good list that would also be useful to you; for me, everything just comes from the principle of least action, symmetry, some constraints, and boundary conditions, but I doubt that helps. Try to come up with a list yourself; that’d probably be a useful exercise. And finally, given the importance of these guiding principles, you can bet that the trickier problems we write will involve one or two of them. For the guiding principles are how we physicists think – and construct problems. In a sense, this makes the exam problems predictable. Study Tips So, I told you what it is graders are looking for in your tests: understandable explanations of what’s going on in each problem. Hence that’s what you should practice doing. Really, that’s how you should be doing your homework. You should have a notebook in which you solve physics problems, and your solutions should look like this: 1. Statement of the problem 2. Explanation of what’s going on 3. Solution and method of solution 4. Discussion of important features...
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