1Tue. Oct. 28, 2008 Physics 208, Lecture 17 1Exam 2 covers Ch. 28-33,Lecture, Discussion, HW, Lab Chapter 28: Electric flux & Gauss’ law Chapter 29: Electric potential & work Chapter 30: Electric potential & field (exclude 30.7) Chapter 31: Current & Conductivity Chapter 32: Circuits (exclude 32.8) Chapter 33: Magnetic fields & forces (exclude 33.3, 33.6, 33.10, Hall effect)Exam 2 is Tue. Oct. 28, 5:30-7 pm, 2103 ChTue. Oct. 28, 2008 Physics 208, Lecture 17 2Electric currentproduces magnetic field Current (flow of electric charges )in wire produces magnetic field. That magnetic field aligns compass needleCurrentMagneticfieldTue. Oct. 28, 2008 Physics 208, Lecture 17 3Law of Biot-Savart Each element of currentproduces a contributionto the magnetic field.rθIds! dB =µo4"Ids #ˆ r r2B out of pagedIdBrTue. Oct. 28, 2008 Physics 208, Lecture 17 4Magnetic field fromlong straight wire:Direction What direction isthe magneticfield from aninfinitely-longstraight wire?I ! dr B =µo4"Idr s #ˆ r r2xyTue. Oct. 28, 2008 Physics 208, Lecture 17 5Current dependenceHow does the magnitude ofthe B-field change if thecurrent is doubled?I ! dr B =µo4"Idr s #ˆ r r2xyA) Is halvedB) QuadruplesC) Stays sameD) DoublesE) Is quarteredTue. Oct. 28, 2008 Physics 208, Lecture 17 6Distance dependenceHow does the magnitude ofthe B-field at 2 compareto that at 1?I ! dr B =µo4"Idr s #ˆ r r2xy12A) B2=B1B) B2=2B1C) B2=B1/2D) B2=4B1E) B2=B1/42Tue. Oct. 28, 2008 Physics 208, Lecture 17 7Why? Biot-Savart says Why B(r)∝ 1/r instead of 1/r2 ? ! dr B =µo4"Idr s #ˆ r r2 ! r r Large contribution fromthis current element.Decreases as 1/r2ISmall contribution fromthis current element.~ independent of rTue. Oct. 28, 2008 Physics 208, Lecture 17 8Long straight wire All current elements produce B out of pagexa! r = x2+ a2rθ! dB =µo4"Ids #ˆ r r2=µo4"Ir2sin$=µo4"Ir2ar=µo4"Iax2+ a2( )3 / 2! B =µoIa4"dxx2+ a2( )3 / 2=#$$%µoI2"aAdd them all up:Tue. Oct. 28, 2008 Physics 208, Lecture 17 9Field from a circular loop Each current element produce dB All contributions add as vectors Along axis, allcomponents cancelexcept for x-compTue. Oct. 28, 2008 Physics 208, Lecture 17 10Magnetic field from loopWhich of these graphsbest represents themagnetic field on theaxis of the loop?BzzxyBzBzBzA.B.C.D.zzzzTue. Oct. 28, 2008 Physics 208, Lecture 17 11Magnetic field from a current loop One loop:field still loops around the wire. Many loops: same effectTue. Oct. 28, 2008 Physics 208, Lecture 17 12Solenoid electromagnet Sequence ofcurrent loops canproduce strongmagnetic fields. This is anelectromagnet3Tue. Oct. 28, 2008 Physics 208, Lecture 17 13Comparing Electric, Magnetic Biot-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 distribution Resulting E is a vectorbut charge (source) is not a vectorTue. Oct. 28, 2008 Physics 208, Lecture 17 14A shortcut: Ampere’s law Integral around closedpath proportional tocurrent passing throughany surface boundedby path. Ampere’s law! B • ds"=µoIclosed pathsurfacebounded bypathI Right-hand ‘rule’: Thumb in direction ofpositive current Curled fingers showdirection integrationTue. Oct. 28, 2008 Physics 208, Lecture 17 15Ampere’s lawSum up component of B around pathEquals current through surface. Ampere’s law! B • ds"=µoIclosed pathsurface bounded by pathI ! r B Component of Balong pathTue. Oct. 28, 2008 Physics 208, Lecture 17 16‘Testing’ Ampere’s law Long straight wire , B⊥r! B r( )=µoI2"rr! B • ds"IB(r)B||dspath hasconstant rpath length= 2πr! B • ds"=µoI2#rds"! B • ds"=µoI2#rds"=µoI2#rds"! B • ds"=µoI2#rds"=µoI2#rds"=µoI2#r2#r =µoICircular pathSurface bounded by pathTue. Oct. 28, 2008 Physics 208, Lecture 17 17Using Ampere’s law Could have used Ampere’s law to calculate BrIB(r)! B • ds" = Bds =" B ds" = B2#r =µoI $ B =µoI2#rCircular pathSurface bounded by pathB||dsB constant on pathpath length= 2πrTue. Oct. 28, 2008 Physics 208, Lecture 17 18Quick Quiz Suppose the wire has uniform current density. Howdoes the magnetic field change inside the wire?A. Increases with rB. Decreases with rC. Independent of rD. None of the aboverB! B"• ds = 2#rB =µoIcut=µoI#r2#R2$ B r(
View Full Document
Unlocking...