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Problem Set #1 - Electricity and Magnetism Physics 2217 and...

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Unformatted text preview: Electricity and Magnetism Physics 2217 and AEP 2170 Spring 2012 Homework 1 Assigned: Monday January 23th Due: Friday January 27rd (only required to hand in Problems 1-4). 1. Problem 1.1 Purcell 2. Problem 1.2 Purcell 3. Problem 1.3 Purcell 4. Finish the "Force on a test charge Q a distance z above the midpoint between a uniform line of total charge q" problem that I started in class. The next few problems are meant to give you an idea of the math that will be required this semester. We will discuss gradients, divergences, and curls over the next couple of weeks, but we will focus on the beautiful physics that these mathematical objects describe rather than answer "how do I calculate x." (I just want to give you an idea of what's ahead.) 5. Let a. Calculate the gradient b. Integrate the gradient of T along the following three paths i. (0,0,0) (1,0,0) (1,1,0) (1,1,1) T d l ii. (0,0,0) (0,0,1) (0,1,1) (1,1,1) P iii. the parabolic path z=x2;y=x 6. Let a. Calculate the divergence b. Integrate the divergence of v over the volume of a cube with sides =2. (the four corners are: 000, 200, 020, 002). c. Integrate v over each surface of the cubic. d. What is the result of integrating over the entire surface? e. Calculate the curl of v. f. Integrate the curl of v over 5 of the 6 sides of the cube (don't integrate over the side in the yz plane intersecting the origin) g. Integrate v over the boundary (0,0,0) (0,1,0) (0,1,1) (0,0,1) (0,0,0) ...
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