Exam4EquationSheet

# Changing magnetic uxrule see a stationary conductor

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Unformatted text preview: ) S B = d£B S y the space nd Sq mmidpoint lar to B windings, L0 c its 0 Outside solenoid S b E d lB = 2proil, inducing a a du (29.10) dl (See Examples turns sense easier to A timedetermined by a right-handr from symmetry axis ed from Faraday’sand Maxwell’s of current (28.15) often (toroid) law N 29.1–29.6.) distance through Bx = with and2is3>2 equations: isuse.changing magnetic ﬂuxrule. (See a stationary conductor, dS E B £ lacement current 2 ocurrent in the coil. dt dl C L 21x + a Examples 28.7–28.10.) 2 i D = POutside the space enclosed by the windings (29.14) m B L 0 0 NI (increasing) S p ^ S r S ying electric ﬁeld generates a displacement current is an induced Within theﬁeld E of nonelectrostatic S of dt electric 2 u enclosed by the windings, d l Tightly space E = B= 1v : B2 (29.7) (circular loop) wound toroidal solenoidthere S 2 d £ B with N turns 2pr e S which as a (toroid) distance r from E he mf actsE = source of magnetic ﬁeld in exactly (29.3)E ﬁeld isunonconservative and axis (displacement current)IdBysymmetry cannot be assoa origin. This r C Outside the spaceS enclosed by the windings BL0 I so ame op f way as conduction current. The relationships m0 NI dt S 947 (all or part dB S ciated with a potential. (See Example 29.11.) of a closed loop moves in a O Bx M z S B= Magnetic 947 The magnet’s induced S weenieldLenz’s law: materials: When that(28.17) materials are Semf Q encl tends to oppose or cancel out multi-electricquantity in electrostatics is electric S orpresent, the magnetization of the material causes 0u tionF damental x and magnetic ﬁelds states magnetic 2a Lenz’s law and theirSsources B (29.18) ﬁeld) I an induced current dA = always + Change in B E motion causes a an additional contribution called IN P x be stated compactly N circular loops) to B. For paramagnetic and diamagnetic materials, m0 is replaced in in four equations, S P0 (center ofMagnetic materials: When magnetic C from present, theBx is often easier to d and the change that caused it. Lenz’s be derived M negative. Charges ofexpressions by law=can m eachhere m isFaraday’s law magnetization of the use. K m is its B changing material and magnetic-ﬁeld they form a completeK w mS xwell’s equations. Together theSsame sign repel m0 , materials arethe permeability of themagnetic material causes 947 S (increasing) B0 (See ExamplesS29.7 and 29.8.) and ﬁelds) . for the relationship of E and B contribution toDisplacement currentfor E Maxwell’s materials, theA time- susan additionalin an magneticB. For paramagneticis deﬁned as xfield through m0 Mreplaced in (Gauss’s law and diamagnetic equations:1. is agnetic i = P d £ E the total (29.6) E = vBL charge The to their systemSis isserved;relative permeability. ﬁelds isolatedsusceptibility xm S (29.14)S ﬁeld, m = Km + G d and S the a S – a displacement current B K m D itsE dt coil, inducing material £ Induced electric ﬁelds: by varying B 0 ﬁeld generates magnetic-ﬁeld expressionsWhen an electricinduced by a is is IB (conductor with length L moves materials = Kemf ,is positive quantities; those of ddiamagnetic materiE rces. ceptibilities for paramagn...
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## This document was uploaded on 03/13/2014.

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