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Use Stokes' Theorem to evaluate curl F- dS where F(r, y, 2) = 4ryzi – ryj + x?yzk and S consists of the top and the four sides (but not the bottom) of the cube with vertices (+2, ±2, +2), oriented outward. Since the box is oriented outwards the boundary curve must be transversed ? when viewed from the top. A parametrization for the boundary curve C seen below from above can be given by: ry(t) r(t) FR(t) rB(t) IL(t) = ( Σ Σ 0

Use Stokes' Theorem to evaluate curl F- dS where F(r, y, 2) = 4ryzi – ryj + x?yzk and S consists of the top and the four sides (but not the bottom) of the cube with vertices (+2, ±2, +2), oriented outward. Since the box is oriented outwards the boundary curve must be transversed ? when viewed from the top. A parametrization for the boundary curve C seen below from above can be given by: ry(t) r(t) FR(t) rB(t) IL(t) = ( Σ Σ 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use Stokes' Theorem to evaluate curl F- dS where F(r, y, 2) = 4ryzi – ryj + x?yzk and S consists of the top and the four sides (but not the bottom) of the cube with vertices (+2, ±2, +2), oriented outward. Since the box is oriented outwards the boundary curve must be transversed ? v when viewed from the top. A parametrization for the boundary curve C seen below from above can be given by: rT(t) rL(t) FR(t) rB(t) rz(t) = ( Σ Σ Σ 0<t<1. FR(t) = ( Σ Σ E ), 0<t<1. r7(t) = (| E ), 0<t< 1. Σ Σ rB(t) = (| Σ 0<t<1. Σ (use the most natural parametrizations) curl F. dS = Σdt curl F. dS Σ
Transcribed Image Text:Use Stokes' Theorem to evaluate curl F- dS where F(r, y, 2) = 4ryzi – ryj + x?yzk and S consists of the top and the four sides (but not the bottom) of the cube with vertices (+2, ±2, +2), oriented outward. Since the box is oriented outwards the boundary curve must be transversed ? v when viewed from the top. A parametrization for the boundary curve C seen below from above can be given by: rT(t) rL(t) FR(t) rB(t) rz(t) = ( Σ Σ Σ 0<t<1. FR(t) = ( Σ Σ E ), 0<t<1. r7(t) = (| E ), 0<t< 1. Σ Σ rB(t) = (| Σ 0<t<1. Σ (use the most natural parametrizations) curl F. dS = Σdt curl F. dS Σ
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