Exam4EquationSheet

# In magnetic field both s field through the b currents

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Unformatted text preview: s law and is often easier toSuse.changing magneti the change that caused B rS mple m0 I changing magnetic Iopposite directions. The magnetic force of currents are in ﬁeld, ¿motion of the loop,.in Magnetic Field both. S field through the B currents and I (See their separation r or B deﬁnition and ExamplesP29.7 and 29.8.) The B Current Distribution oint Magnetic-FieldIMagnitudeS S B= (28.9) S B oil, inducing a I c per unit length between the this relationship. (See Example S B om a 2pr(See Examplesampere is based onconductors depends on their the 29.1–29.6.) B S B S c coil m0 I B currents I and ¿ and their separation The table lists magnetic ﬁelds caused by several current distributions. In each case the con- urrent in the E Magnetic ﬁelds due toI current distributions: r. The deﬁnition of S B magS E =I vBL Distance r from conductor (29.6) B= B tional emf: Long, straight conductor a magnetic.on this relationship. (See Example If a conductor moves 28.5.)is based ﬁeld, in S S S B ductor the ampere current I is carrying 2pr B netic v B 947 (conductor S S length L moves in uniwith S yB otional emf is induced. Ia 228.5.) nd m0 (See Examples 29.9 and S B irecCurrent Distribution (28.15) PL and S Magnetic Field F = qvB F = Magnetic-Field Magnitude qE S Bx = form B ﬁeld, oint in v both 947 perpendicum0 Ia 2 10.) o2 y + dl law of Biot and The m0 Ia 2 + 21 loop a 223>2 a 28.3 B =– Circular x + of radius Magnetic ﬁeld of a current loop:SOn axis each other) p lar to B and to of loop ^ r a q m b 21 I B (28.15)0x 2 + a 223>2 S of Savart allows us to calculate the magnetic ﬁeld2 u conductorx = proS 2 2 3>2 (circular loop) straight conductor dl Long, law: Lenz’s Distance r from B= 21x 2 oppose orLcancel outpr Lenz’s Magnetic ﬁeld law the axisthat circular conducting2loopBof always tends + a 2 an to S p2 Change in B ^ he r 2 au Sr S of a states loop: induced current or emf m0 Ia duced along current of a The law of Biot and d y S S m0 I (for N loops,ymultiply theseu (circular loop) (29.6) E = vBL use. 2S l (29.7) S (28.15) If a ﬁeld, the Savartradius a us to calculate the The ﬁeld dependsdon moves in a Lenz’s I. = Atbe ﬁeldof loop to I magnetic derived p S B dB m0 NI change that caused it.Motionallaw can1v conductor thedB Bx = magnetic 2 3>2 often easier B = center 2 S allows carrying current Eemf:C O : B2 pro-from Faraday’s law and is 22 a z 2a expressions a u (28.17) Bx = d £ (conductor=with m0 Ia I L dl by N) in uni- u y S B length moves r (increasing) p2 x S the(See Examples 1x +and2 ^ r Circular loop of radius axis ofmotional conducting axis of loop On of 29.9NI ulti(See duced distanceax alongathe circular emf centerBclosedloop along the a axis (all or part of a loop I u ed emf m0 SB S2 2a m0 II ¿ B Examples 29.7 and 29.8.) Ifrom theis induced. ofloop moves in a loop) dB F rs: 2 S (circular O x S2 21 + S 3>2 E=(29.3) F Bx = form B (28.17)0xIandav2bothaperpendicu-dB u ﬁeld,mL r z = of N (28.11) 29.10.) S ﬁeld) I the ﬁeld is o the radius ta carrying current thereB ﬁeld depends S P multite o...
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## This document was uploaded on 03/13/2014.

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