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Introductory homework to the Spring semester. Covers a broad spectrum of topics that will be relevant from E&M 1
Typology: Assignments
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Show/explain your work. We grade homework for clarity of explanation as much as for mere correctness of final answers. Use whatever resources help you learn (e.g. Griffiths or other texts, peers, office hours.) But, what you turn in must be your work , reflecting your understanding. Copying is not considered “collaboration”. Please reference all sources you use. Commercial homework sites and bots are notorious for poor solutions, and they provide little (or negative) value to you. Use your good judgment. Ask if you have questions about what is useful (and appropriate). Scan and upload a single pdf. See Canvas for details. We use Gradescope in Canvas. You tell Gradescope which of your pdf pages contain which problems. (Every week, do it with care.) Remember that an (overworked, underpaid) grad student grades your homework. They do their best, please help them by scanning carefully, writing neatly, organize your work so a human can follow. Look at your pdf – if pages are hard to read, please rescan and try again. Thanks. Firm deadline is Thurs night (i.e, before Friday@8 AM) After solutions post Fri@ 8AM, you still have one day+ to rework any problems you made any mistakes on. See Canvas for details. You can’t rework problems you did not make a genuine effort on for the Thursday deadline. If you do any rework corrections, you have to rescan and resubmit the entire set, not just the problems you fixed up. The final (optional) rework deadline is Sat noon. I drop one HW for everyone automatically. Email if circumstances beyond your control prevent you from doing a homework on time. (If you are partially finished, much better to submit what you have done than nothing at all.) Please reach out for assistance when you need it!
1.) ( 10 pts) Please do this FIRST, before you work on the rest of the homework. Go to https://tinyurl.com/CUB-Sp25pre and do your best. Don’t look up anything, do it on your own – and don’t stress! If you don’t remember, make a guess or leave it blank. You will NOT BE GRADED FOR CORRECTNESS , full credit on this question simply for trying. Use it to guide your review of 3310. If there are questions you feel confused/unsure about, indicate on the homework pdf you turn in WHICH question(s) bug you. (They are labeled “Q1”, “Q2”, etc) The remaining homework (below) is also meant to help you review – these will be graded. 2.) For each of the five vector fields sketched below.... a ) ( 5 pts) Which of them have nonzero divergence somewhere? (If the divergence is nonzero only at isolated points, which point(s) would that be? ) Briefly but clearly explain your reasoning. b ) ( 5 pts) Which of the following fields have nonzero curl somewhere? (If the curl is nonzero only at isolated points, which point(s) would that be? ) Briefly but clearly explain your reasoning. The first 3 figures are all “cylindrical” fields, i.e they are uniform if you move directly out of the page. i. (Arrows are all same length, and azimuthal) ii. iii. (The next two fields are spherical/“radial” fields if you extend to 3-d: they point away from the origin everywhere) iv. (Note: Arrows grow in length ∝ 𝒓𝟐 ) v. (Note: Arrows decrease in length as 1/r^2 , like a Coulomb field) (HW continues on next page)