Electromagnetic Field Theory: A Problem Solving Approach Part 63 docx

... (39) Although the waves are attenuated, all frequencies propagate at the same phase and group velocities as for a lossless line ) 1 VP = =-I- do, 1 (40) Vg = dk, Since all ... voltage and current waves decay as they propagate. Because the governing equations of Section 8-1-3 are linear with constant coefficients, in the sinusoidal steady state ....

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... differentiations V. (VxA) a, aA, aA, \ a aA aA) a aA, aA\ -ax\y az / y az ax I az\ ax ay / xa 2 A, a 2 A , a 2 A, 2 A a 2 A, a 2 Ax ( -\xay avax \ayaz azay) \azax ax(z where ... 39 curl operation: i. i, i, V x (Vf)= det a a ax ay az af af af ax ay az .= (•- •L f . +,( af a/ 2 f) + i(.I2- a 2 f).0 ayaz azay azax axaz axay a...

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... A. Those field lines that start at infinity where the charge is injected and that approach the sphere with negative radial electric field, deposit charged particulate, as ... electric field radially inward charge. (a) If the total charge on the sphere starts out as negative charge with magnitude greater or equal to the critical within the...

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... derivatives of w are aw dw az dw au .Ov ax dz ax dz ax+ ax aw dw az .dw au av ay dz ay dz -y ay show that u and v must be related as au av au av ax Oy' Oy ax A ... r /a? Are these forces equal? (e) Repeat (a) -(c), if rather than free charge, the slab is a permanently polarized medium with polarization P= Po sin axi, 8. Consider...

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... the smaller contour now encloses a fraction of the current. O)i, +a sin 0i, r^ The Vector Potential 341 with associated magnetic field B=VxA (1 aA, A aAA . 1I a aAr " ... A, as we can add the gradient of any term to A and not change the value of the magnetic field, since the curl of the gradient of any function is always zero: A-...

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... of of Faraday's law (a) if L R V/ R 1 S Rr L + - (b) Figure 6-15 (a) A conducting disk rotating in an axial magnetic field is called a homopolar generator. (b) In addition ... rather than decay with time with any small perturbation, as illustrated in Section 6-3-3b. 6-3-3 Faraday's Disk (Homopolar Generator)* (a) Imposed Magnetic...

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... again, the H parallel to the interface polarization is entirely trans- mitted while the E parallel to the interface polarization is partially reflected and partially transmitted. ... a transmitted field that decays with distance as a nonuniform plane wave. However, there is no time-average power carried by this evanescent wave so that all the t...

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... evaluated by realizing that as r - 0 there can be no propagation delay effects so that the potential should approach the quasi-static Coulomb potential of a point charge: Q(Q) ... the negatively traveling wave solution as there are no sources for r >0 so that all waves emanate radially outward from the point charge at r =0. The arbitrary...

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... placed along the z axis a distance 2a apart. The dipoles have the same length i · I Problems 697 y while the currents have equal magnitudes but phase difference X. (a) What ... (huhA)+ (huhAw) huhh, au av aw 1 8a( hA4) 8(hA,) (V x A) , = [ a- hAw) a( A hh, av aw 25. (a) rQp = i, (b) iQ= rQ i - 5i, + 2i rQP -30 5i. + iy (c)n -+ Chapter 2...

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... VfxA+fVxA (V x A) x A = (A V )A - 'V (A . A) Vx (Vx A) = V(V - A) - V A INTEGRAL THEOREMS Line Integral of a Gradient Vf dlI =f(b) -f (a) Divergence Theorem: f V-AdV= ... magnetic scalar potential, 365 spherical coordinates, 284 Laplacian of reciprocal distance, 73-74 Larmor angular velocity, 316 Laser, 517 Law of sines and cosines,...

Ngày tải lên: 03/07/2014, 02:20