Let S be the closed surface that consists of the hemisphere x² + y² + z² = 1, z ≥ 0, and its base x² + y² ≤ 1, z = 0. Let E be the electric field defined by E(x, y, z) = 7xi+ 7yj + 7zk. Find the electric[₁₁²flux across S. HINT: Break S into two pieces S₁ and S₂ and evaluate1E. dS and√5₂E dS separately. Give this surface an outer normal.

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Let S be the closed surface that consists of the hemisphere x² + y2 + z2 = 1, z ≥ 0, and its base x² + y² ≤ 1, z = 0. Let E be the electric field defined by E(x, y, z) = 7xi+ 7yj + 7zk. Find the electric flux across S. HINT: Break S into two pieces S₁ and S₂ and evaluate SE · ds and affe. E dS separately. Give this surface an outer normal.

Let S be the closed surface that consists of the hemisphere x² + y2 + z2 = 1, z ≥ 0, and its base x² + y² ≤ 1, z = 0. Let E be the electric field defined by E(x, y, z) = 7xi+ 7yj + 7zk. Find the electric flux across S. HINT: Break S into two pieces S₁ and S₂ and evaluate SE · ds and affe. E dS separately. Give this surface an outer normal.

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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Question

Let S be the closed surface that consists of the hemisphere x² + y² + z² = 1, z ≥ 0, and its base x² + y² ≤ 1, z = 0. Let E be the electric field defined by E(x, y, z) = 7xi+ 7yj + 7zk. Find the electric
[₁₁²
flux across S. HINT: Break S into two pieces S₁ and S₂ and evaluate
1
E. dS and
√5₂
E dS separately. Give this surface an outer normal.

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