W9_parallel_resonance.eps
0.1. POTENTIAL ENERGY OF A MAGNETIC DIPOLE 219 x y ∆φ L ∆L z(out) Figure 76: The torque causesL⊥to precess around thez-axis (out ...
220 Week 6: Moving Charges and Magnetic Force available to physicians practicing modern medicine. It is also not terribly easy t ...
0.1. POTENTIAL ENERGY OF A MAGNETIC DIPOLE 221 randomsuperpositions of those states, ones that are as likely to be eigenstates o ...
222 Week 6: Moving Charges and Magnetic Force Homework for Week 6 Problem 1. Physics Concepts Make this week’s physics concepts ...
0.1. POTENTIAL ENERGY OF A MAGNETIC DIPOLE 223 Problem 4. B m R N turns, carrying I θ A circular loop of wire with radiusR,N tur ...
224 Week 6: Moving Charges and Magnetic Force Problem 6. Q,M L ω A nonconducting rod of total massMand lengthLhas a chargeQunifo ...
0.1. POTENTIAL ENERGY OF A MAGNETIC DIPOLE 225 Problem 7. R, M, Q ω z t A disk of radiusRand thicknesst, with uniform charge den ...
226 Week 7: Sources of the Magnetic Field Advanced Problem 9. A semi-infinite thin solenoid aligned with (say) the negativez-axi ...
Week 7: Sources of the Magnetic Field (Est 2/18-2/25) Noisolated magnetic monopoleshave been experimentally observed, in spite ...
228 Week 7: Sources of the Magnetic Field The field of a long straight wire carrying a currentIis: B~=^2 kmI r φˆ (488) whereφ ...
Week 7: Sources of the Magnetic Field 229 If there is, then we would expect the field of a collection of “magneticmonopolar” cha ...
230 Week 7: Sources of the Magnetic Field Magnetic field lines must formclosed loops. As we’ll shortly see, those closed loops ...
Week 7: Sources of the Magnetic Field 231 charges we didn’t find any. Yet magnetic fields exist in abundance; otherwise how coul ...
232 Week 7: Sources of the Magnetic Field r B (out of page) B (into page) q v θ Figure 77: The geometry of the magnetic field li ...
Week 7: Sources of the Magnetic Field 233 q 1 1 q 2 v 2 v r 12 F 12 21 Bin B, F = 0 Figure 78: Newton’s Third Law fails for this ...
234 Week 7: Sources of the Magnetic Field A dl r q θ Ι vd dB (in) Figure 79: The microscopic model of conduction used to derive ...
Week 7: Sources of the Magnetic Field 235 r r r − r dl I 0 dB 0 Figure 80: The Biot-Savart Law in general coordinates. Wow! That ...
236 Week 7: Sources of the Magnetic Field a general point on thex-axis, and no matter where we locate it we can do an integral b ...
Week 7: Sources of the Magnetic Field 237 Example 7.4.2: Field of a Circular Loop on its Axis dl x y z z r dB I a φ φ dBz θ dθ d ...
238 Week 7: Sources of the Magnetic Field However, one day you might need toshowthat the⊥field vanishes thehard wayby actually i ...
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