Use Stokes' Theorem to Calculate the Circulation of the Field $\mathbf { F } = 3 x \mathbf { i } + 2 x \mathbf { j } + 7 \mathrm { zk } ; \mathrm { C }$

question 61

Multiple Choice

Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction.
- $\mathbf { F } = 3 x \mathbf { i } + 2 x \mathbf { j } + 7 \mathrm { zk } ; \mathrm { C }$ : the cap cut from the upper hemisphere $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } = 16 ( \mathrm { z } \geq 0 )$ by the cylinder $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } = 4$

• A) \(3 \pi\)
• B) \(2 \pi\)
• C) \(4 \pi\)
• D) \(8 \pi\)

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