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Unformatted text preview: D = (29.10) BRIDGING, PROBLEM Magnetic Field of a Charged,:Rotating Dielectric Disk (Gauss’s 947 lar 1 uctor, 2 C At t dt way conductionucurrent. Field of a Charged, Rotating Dielectric m Ia 2 law for B fields) the same vz as dvz ¢ C BRIDGING PROBLEM MagneticSThe relationships S 2 Disk d 0 d £ Bpart S (allS increasing a closed atic ular Onaz = betweenqelectric and magnetic fieldsEandl their sources of inducedDuloop movesencla d = - BorS = in axis lim 0 of loop = S S S S dis- A thin dielectric ƒ ¢1tq2with dt = a has a total charge +Sfield)2 on 1B 4. (29.21) B Q it take the charge found in step£3 to make a 1S disk ƒ radius dt 2 E dt F ¢t BQ distribC e assoS 2 3>2 How u2 = does long E dA E can be stated compactly in four (21.2) called second F = A thin dielectric disk with radius a equations,charge + Q distrib- 4. How long P 21it 2 +Ba dS(29.18) i C in step 3 E b make a 2 = found + P d to has a total does x take the chargem0 a l u1 0 uted uniformly over2its surface. It rotates n(Faraday’s law) about (9.5), timestimes complete (9.6) per per second 4pP0 r equations.surface. It rotatesform a second about Ccomplete trip around the rotating ring? Use this0 todtfind the curuted uniformly over its Together they n x around C rotating ring? Use this to encl the Maxwell’s r complete trip S Magnetic-Field Magnitude find the curangu- Point in Magnetic Field S S an axis an axis perpendicular to perpendicular to the surface of the disk disk and passing (Gauss’s of the rotating ring. N l and passing O rent law rotating I (for sely rent of the for mfields) ring. (29.20) multiply these basis of surface of their q S G Induced electricfor Find the an emfthe field at by acenter of S disk. is E and the the relatedAt = vBL center. the When magnetic induced B fields toS the dS 1disk.d £ BUse a result= E 0Section 28.5 oops, E (29.6) E center through its offields: looprelationshipmagnetic field at the centerEof the = - S5. 5. Use aB (29.10) Section 28.5 tolaw981 the displacement from eld, l 1Find 2 through its center. S g the changing£ E + v flux+ a t athe result from (Ampere’sto determine themagnetic field determine including magnetic field magnetic u 1 du = sources. t through (9.11) maI timev dt that this ring produces at the center of by disk. C S S F1 on 2 20 expressions the N) for (conductor S 0zlength Lz S stationary conductor, B i D = P an 0 8.988 * 2field N ofm > uni(29.14) have Distance=r withelectric10 9moves2inC2 there isS dtinduced E B that2 this ring produces at the center of theincreasing dA B 0 rrent S from conductornonelectrostatic = result current) 5 to find S disk. magnetic field q =your result from Sstep(29.19) Bthetotal magnetic field F = qvB FCIntegrate q 6. =6. EIntegrate your pr fromstep 5 find the total form P(constantand v both perpendicu4p B0 field, L ion. SOLUTION GUIDEaGUIDE SOLUTION E 2 S S (displacement current)z only) + .ctly SI origin. This field is nonconservative and cannot be assoIn S r from rings m with r from r = r= from– allall ringsB 0 I radiifrom S = 0 toE£ = a. . lar towith a MasteringPhysics® study areaVideo Video Tutor solution. and to eachstudy area for a for other) BSee potential. (See Example 29.11.)a Tutor solution. + a q (Gauss’s law forwith radii S dr B a ciated fields) hips b See MasteringPhysics® r 29 SUMMARY 29 SUMMARY 0 29 SUMMARY # # 0 ARY # 29 SUMMARY 0 # # # # RY # 0 RY # # # # The table lists magnetic fields caused by several current distributions. In each case the con# # RY # # # # # The table# lists magnetic fields caused by several current distributions. In each case the con# # # # # # e lists magnetic fields caused by several current distributions. In each case the con-...
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This document was uploaded on 03/13/2014.

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