Lecture 17 mar11 - Lecture 17 Ampere’s Law and Magnetic...

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Unformatted text preview: Lecture 17 Ampere’s Law and Magnetic Materials Deadline for dropping a course is Friday March 14 Ampere’s Law Biot-Savart Law is analogous to Coulomb’s Law and Ampere’s Law is analogous to Gauss’s Law for Electricity, i.e. they both tell us about the source of the field—they tell us the generators of the fields Since B field lines are LOOPS that tend to go around currents/moving charge you might expect Ampere’s law to involve a line integral of B…………. Let’s consider first a specific case with simple integrals, a long straight wire , and then generalize. 2 ˆ r r dq k E d = 2 ˆ 4 r r l Id B d × = & π μ For ∞ straight wire r I B π μ 2 = I dl r I l d B r r 1 1 1 2 μ π μ = = ⋅ ∫ ∫ 4 4 = +- + = ⋅ ∫ I I l d B path μ μ r 1 r 2 Integrate CW around a circular path of r 1 Now for a path at r 2 we get the same result, the path integral doesn’t depend on r……. Now consider a 3 rd path not around I…... enclosed path closed I l d B μ = ⋅ ∫ This result is general: B 1 B 2 I dl r I l d B r r 2 2 2 2 μ π μ = = ⋅ ∫ ∫ (See fig. 28.17) in text Ampere’s Law: ∫ ∫ ⋅ = = ⋅ surface bounded any enclosed path closed A d j I l d B μ μ 1. Line integral of B around any closed path = μ times net current penetrating any surface bounded by the path. 2. Alternate form: enclosed I l d B path closed μ = ⋅ ∫ 1. With slight modification for time varying E fields Ampere’s Law will become Maxwell’s 4 th equation. 2. Ampere’s law is perfectly general but, like Gauss’s law for electricity it is not very useful in calculating B fields unless the symmetry is high Andre Marie Ampere (French 1775-1836) Andre Marie Ampere (French 1775-1836) Andre Ampere AC / DC Ohm's Law Watch Tired of fumbling for those hard to remember AC and DC Ohm's law & Power formulas http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Ampere.html In the early 1820s, Ampère attempted to give a combined theory of electricity and magnetism after hearing about experimental results by the...
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Lecture 17 mar11 - Lecture 17 Ampere’s Law and Magnetic...

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