ampere's law

ampere's law - Andr-Marie Ampre (1775-1836) Last Time...

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1 1 Magnetic Field & Current: Ampere’s Law André-Marie Ampère (1775-1836) This lecture: HRW 29.4-29.6 Next time: Midterm Review Next Monday, sample midterm review, 4:40 in 117 Osmond 2 Last Time Electric currents create magnetic fields Calculate magnetic field using the Biot-Savart Law: it applies to ANY current Simple cases: Infinite straight wire Circular loop of wire Ampere’s Law: relates the integral of B around a closed loop to the current enclosed Like Gauss’ Law, it makes for a much easier calculation when there is a lot of symmetry. Today 3 Ampere’s Law Gauss’ Law: = Surface Closed 0 enc ε Q A d E r r Consider any closed LOOP, C. Integrate the component of B along the loop. This is proportional to the TOTAL current passing through a surface enclosed by C The sign of i enc is given by the RHR -- curl fingers around the loop in the direction you are traversing it. Any i in the direction of your thumb is “positive”, opposite i is negative. Ampere’s Law: = Loop Closed enc 0 i μ s d B r r i ds 4 Calculate B from an infinite straight wire with current i, using Ampere’s Law. Ampere’s Law for a Long Wire There is a lot of symmetry: every point on an infinite wire is identical B depends only on r, not on x ˆ z ˆ x ˆ y = C enc 0 i μ s d B r r Ä = 0 μ i B 2 π r = B2 π r 0 =+ μ i Ampere’s Law = C C ds B s d B r r symmetry r Choose a circular loop C, the wire B is the same everywhere on the loop The angle between B and ds = 0.
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This note was uploaded on 04/05/2008 for the course PHYS 212L taught by Professor Huang,tai-yin during the Spring '07 term at Penn State.

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ampere's law - Andr-Marie Ampre (1775-1836) Last Time...

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