# For the inscribed and circumscribed circles and then

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for the "inscribed" and "circumscribed" circles and then average. How good an approximation does that turn out to be? (Can you think of a better way?) a Circumscribed inscribed ωB? z σR B? z y
Phys 3310, HW #12, Due in class Wed Apr 10 Q4. AMPERES LAW - THEMES AND VARIATIONS Consider a thin sheet with uniform surface current density K0ˆ A) Use the Biot-Savart law to find B(x,y,z) both above and below the sheet, by integration. Note:The integral is slightly nasty. Before you turn to Mathematica - simplify as much as possible! Set up the integral, be explicit about what curly R is, what da' is, etc, what your integration limits are, etc. Then, make clear mathematical and/or physical arguments based on symmetry to convince yourself of the directionof the B field (both above and below the sheet), and to argue how B(x,y,z) depends (or doesn't) on x and y. (If you know it doesn't depend on x or y, you could e.g. choose x=y=0 to simplify... But first you must convince us that's legit!) B) Now solve the above problem using Ampere's law. (Much easier than part a, isn't it?) Please be explicit about what Amperian loop(s) you are drawing and why. What assumptions (or results from part a) are you making/using? (Griffiths solves this problem, so don't just copy him, work it out for yourself!) C) Now let's add a second parallel sheet at z=+a with a current running the other way. (Formally, this means J'=K0δ(za) ˆ x . Do you understand this notation?) Use the superposition principle (do NOT start from scratch or use Ampere's law again, this part should be relatively quick) to find Bbetweenthe two sheets, and also outside(above or below) both sheets.Does this remind you of a familiar electrostatics problem at all? How?D) Griffiths derives a formula for the B field from a solenoid (Example 5.9) Rewrite his answer x
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