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Unformatted text preview: PHYS 411 (Fall 2011): Electricity and Magnetism Homeworks 1 Homework 1 (due Tuesday, September 13 in lecture or in folder outside Room 4119 by 5 pm.) Print your name and sign (with date) the Honor Pledge (which covers all assignments): I pledge on my honor that I will not give or receive any unauthorized assistance (including from other persons and online sources) on all examinations and homework assignments in this course. 2 Homework 2 (due Tuesday, September 13 in lecture or in folder outside Room 4119 by 5 pm.) 2.1 Transformation of vectors Problem 1.10 from Griffiths. 2.2 Gradient in Cartesian coordinates Problem 1.12 from Griffiths. 2.3 Stokes theorem in Cartesian Coordinates Problem 1.33 from Griffiths. 2.4 Gradient theorem and Laplacian in spherical polar coordi- nates Problem 1.40 from Griffiths. 2.5 Divergence theorem and curl in cylindrical coordinates Problem 1.42 from Griffiths. The surface/area elements can be worked out as combination of the three displacement elements given in Eq. 1.76 of Griffiths. Note that the surface/area element depends on the orientation of surface so that you might need different ones for the various surfaces of Fig. 1.43 of Griffiths. Also, check that the dimension of area element you are using here (and always) is length 2 . 2.6 Delta function and integration by parts Problem 1.48 from Griffiths. 2.7 Electric field due to charged ring (i) Problem 2.5 from Griffiths. (ii) Check that your formula is consistent with what you would expect for z r . 2.8 Electric field due to charged spherical surface (i) Problem 2.7 from Griffiths. ( Hint : When you integrate over the surface charge, make sure that you use the appropriate area element: see below Eq. 1.69 of Griffiths. If you would like to look at a example of such an integration, go to Example 2.7 of Griffiths.) ( Hint : You might wish to simplify the calculation by massaging the surface integral into a sum over (thin) rings of charge which make up the spherical surface and then using the result of the previous problem for electric field due to a ring of charge.) (ii) Check that your formula is consistent with what you would expect for z R . 3 Homework 3 (due Tuesday, September 20 in lecture or in folder outside Room 4119 by 5 pm.) 3.1 Gausss law for spherical shell Problem 2.11 from Griffiths. You calculated the same electric field by brute force, i.e., using Eq. 2.7 of Griffiths hopefully, you are now convinced of the usefulness Gausss law! 3.2 Gausss law for solid sphere Problem 2.12 from Griffiths. I did not assign problem 2.8 from Griffiths as homework so that it is OK if you are not able to do the 2nd part of this problem, i.e., comparing your answer to that of problem 2.8....
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