Exam 2 covers Ch. 27-32, Lecture, Discussion, HW, LabElectric current produces magnetic fieldLaw of Biot-SavartMagnetic field from long straight wire: DirectionCurrent dependenceDistance dependenceWhy?Long straight wireForces between currentsForce between current-carrying wiresField from a circular loopMagnetic field from loopMagnetic field from a current loopSolenoid electromagnetComparing Electric, MagneticA shortcut: Ampere’s law‘Testing’ Ampere’s lawUsing Ampere’s lawQuick QuizBuilding a solenoidAmpere’s law for the solenoidWed. Mar. 26, 2008 Physics 208, Lecture 17 1Exam 2 covers Ch. 27-32,Lecture, Discussion, HW, LabChapter 27: Electric flux & Gauss’ lawChapter 29: Electric potential & workChapter 30: Electric potential & field Chapter 28: Current & ConductivityChapter 31: CircuitsChapter 32: Magnetic fields & forces(exclude 32.6,32.8,32.10)Exam 2 is Wed. Mar. 26, 5:30-7 pm, 2103 Ch: Adam(301,310), Eli(302,311), Stephen(303,306), 180 Science Hall: Amanda(305,307), Mike(304,309), Ye(308)Wed. Mar. 26, 2008 Physics 208, Lecture 17 2Electric current produces magnetic fieldCurrent (flow of electric charges )in wire produces magnetic field.That magnetic field aligns compass needleCurrentMagnetic fieldWed. Mar. 26, 2008 Physics 208, Lecture 17 3Law of Biot-SavartEach element of current produces a contribution to the magnetic field.rIds€ dB =μo4πIds ׈ r r2B out of pagedIdBrWed. Mar. 26, 2008 Physics 208, Lecture 17 4Magnetic field from long straight wire:DirectionWhat direction is the magnetic field from an infinitely-long straight wire?I € dr B =μo4πIdr s ׈ r r2xyWed. Mar. 26, 2008 Physics 208, Lecture 17 5Current dependenceHow does the magnitude of the B-field change if the current is doubled?I € dr B =μo4πIdr s ׈ r r2xyA) Is halved B) QuadruplesC) Stays sameD) DoublesE) Is quarteredWed. Mar. 26, 2008 Physics 208, Lecture 17 6Distance dependenceHow does the magnitude of the B-field at 2 compare to that at 1?I € dr B =μo4πIdr s ׈ r r2xy12A) B2=B1B) B2=2B1C) B2=B1/2D) B2=4B1E) B2=B1/4Wed. Mar. 26, 2008 Physics 208, Lecture 17 7Why?Biot-Savart saysWhy B(r) 1/r instead of 1/r2 ? € dr B =μo4πIdr s ׈ r r2 € r r Large contribution from this current element.Decreases as 1/r2ISmall contribution from this current element.~ independent of rWed. Mar. 26, 2008 Physics 208, Lecture 17 8Long straight wireAll current elements produce B out of pagexa€ r = x2+ a2r€ dB =μo4πIds ׈ r r2=μo4πIr2sinθ=μo4πIr2ar=μo4πIax2+ a2( )3 / 2€ B =μoIa4πdxx2+ a2( )3 / 2=−∞∞∫μoI2πaAdd them all up:Wed. Mar. 26, 2008 Physics 208, Lecture 17 9Forces between currentsWhich of these pairs of currents will attract each other?A. AB. A & CC. BD. A & BA B CWed. Mar. 26, 2008 Physics 208, Lecture 17 10Force between current-carrying wiresAttractive for parallel currents.Repulsive for antiparallel currentsWed. Mar. 26, 2008 Physics 208, Lecture 17 11Field from a circular loopEach current element produce dBAll contributions add as vectorsAlong axis, allcomponents cancelexcept for x-compWed. Mar. 26, 2008 Physics 208, Lecture 17 12Magnetic field from loopWhich of these graphs best represents the magnetic field on the axis of the loop?BzzxyBzBzBzA.B.C.D.zzzzWed. Mar. 26, 2008 Physics 208, Lecture 17 13Magnetic field from a current loopOne loop: field still loops around the wire.Many loops: same effectWed. Mar. 26, 2008 Physics 208, Lecture 17 14Solenoid electromagnetSequence of current loops can produce strong magnetic fields.This is an electromagnetWed. Mar. 26, 2008 Physics 208, Lecture 17 15Comparing Electric, MagneticBiot-Savart: calculate B-field from current distribution.Resulting B-field is a vector, and…complication: current (source) is a vector!Coulomb: calculate E-field from charge distributionResulting E is a vector but charge (source) is not a vectorWed. Mar. 26, 2008 Physics 208, Lecture 17 16A shortcut: Ampere’s lawIntegral around closed path proportional to current passing through any surface bounded by path.Ampere’s law€ B • ds∫= μoIclosed pathsurface bounded by pathIRight-hand ‘rule’: Thumb in direction of positive currentCurled fingers show direction integrationWed. Mar. 26, 2008 Physics 208, Lecture 17 17‘Testing’ Ampere’s lawLong straight wire , Br € B r( )=μoI2πrr€ B • ds∫IB(r)B||dspath has constant rpath length = 2πr€ B • ds∫=μoI2πrds∫€ B • ds∫=μoI2πrds∫=μoI2πrds∫€ B • ds∫=μoI2πrds∫=μoI2πrds∫=μoI2πr2πr = μoICircular pathSurface bounded by pathWed. Mar. 26, 2008 Physics 208, Lecture 17 18Using Ampere’s lawCould have used Ampere’s law to calculate BrIB(r)€ B • ds∫ = Bds =∫ B ds∫ = B2πr = μoI ⇒ B =μoI2πrCircular pathSurface bounded by pathB||dsB constant on pathpath length = 2πrWed. Mar. 26, 2008 Physics 208, Lecture 17 19Quick QuizSuppose the wire has uniform current density. How does the magnetic field change inside the wire?A. Increases with rB. Decreases with rC. Independent of rD. None of the aboverB€ B∫• ds = 2πrB= μoIcut= μoIπr2πR2⇒ B r( )=μoI2πR2rWed. Mar. 26, 2008 Physics 208, Lecture 17 20Building a solenoidWed. Mar. 26, 2008 Physics 208, Lecture 17 21Ampere’s law for the
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