52 contour paths for a problem 352 and b problem 353

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Unformatted text preview: ular contour shown in Fig. P3.52(a), and n C (b) S (∇ × B) · d s over the surface of the semicircle. y y 2 2 L2 1 -2 L3 0 L1 (a) x 2 0 L2 L3 L4 L1 1 2 x (b) Figure P3.52: Contour paths for (a) Problem 3.52 and (b) Problem 3.53. Solution: (a) B · dl = n L1 B · dl + L2 B · dl + L3 B · d l, ˆ ˆ ˆ ˆ ˆ B · d l = (rr cos φ + φ sin φ ) · (r dr + φ r d φ + z dz) = r cos φ dr + r sin φ d φ , 2 L1 B · dl = = L2 B · dl = r =0 12 2 +0 2r r =0 2 r =2 = 0+ L3 B · dl = = r cos φ dr φ =0, z=0 π + z=0 (−2 cos φ )|π =0 φ 0 r =2 1 − 2 r2 φ =0 r sin φ d φ z=0 = 2, r cos φ dr r cos φ dr 0 +0 r =2 B · d l = 2 + 4 + 2 = 8. n 0 + φ =0 r sin φ d φ r=2, z=0 = 4, φ =π ,z=0 = 2, π + φ =π r sin φ d φ z=0 (b) ˆ ˆ ∇×B = ∇×(rr cos φ + φ sin φ ) 1∂ ∂ ˆ ∂ (r cos φ ) ...
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This homework help was uploaded on 02/20/2014 for the course EEC 130 at UC Davis.

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