# DQ9A_solution - Discussion Question 9A P212 Week 9 Amperes Law in a Nutshell Amperes Law is the magnetic analogue of Gauss Law Q E dA = enc Gauss

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Discussion Question 9A P212, Week 9 Ampere’s Law in a Nutshell Ampere’s Law is the magnetic analogue of Gauss’ Law. Gauss’ Law relates the integral of the electric field through a closed “Gaussian surface ” to the total charge enclosed by that surface. Ampere’s Law relates the integral of the magnetic field around a closed “Amperian loop ” to the total current enclosed by that loop. Just like Gauss’ Law, Ampere’s Law provides the simplest method for determining the magnetic field of a known current distribution … but it can only be used in a practical way if the problem has enough symmetry . It all boils down to choosing a suitable Amperian loop . The mathematical curve we choose has to have these properties: The magnetic field must have a constant magnitude on our curve. The magnetic field must make a constant angle with our curve (or portions thereof). Otherwise, we’ll never be able to extract the B field we want from that line integral! The other part of the procedure is finding the current enclosed by our Amperian loop: In your mind, imagine that the Amperian curve is a loop of coat-hanger wire, and

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## This note was uploaded on 06/16/2011 for the course PHYS 212 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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DQ9A_solution - Discussion Question 9A P212 Week 9 Amperes Law in a Nutshell Amperes Law is the magnetic analogue of Gauss Law Q E dA = enc Gauss

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