The two surfaces shown have the same boundary. Suppose they are both oriented so that the light side (the inside) is the "positive" side. Is the following reasoning correct? Justify your answer. "Since S₁ and S₂ have the same (oriented) boundary, the flux integrals SS, G. dS and ₂ G. ds must be equal for any vector field G. Therefore, you can compute any flux integral using the simpler surface."
The two surfaces shown have the same boundary. Suppose they are both oriented so that the light side (the inside) is the "positive" side. Is the following reasoning correct? Justify your answer. "Since S₁ and S₂ have the same (oriented) boundary, the flux integrals SS, G. dS and ₂ G. ds must be equal for any vector field G. Therefore, you can compute any flux integral using the simpler surface."
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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Transcribed Image Text:3. The two surfaces shown have the same boundary. Suppose they are both oriented so that the light
side (the inside) is the "positive" side. Is the following reasoning correct? Justify your answer.
"Since S₁ and S₂ have the same (oriented) boundary, the flux integrals ff, G-dS and ₂ G. dS
must be equal for any vector field G. Therefore, you can compute any flux integral using the simpler
surface."
S₁
S2
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