Find the Flux of the Curl of Field F Through

question 53

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $$\mathbf { F } = ( \mathrm { z } - \mathrm { y } ) \mathbf { i } + ( \mathrm { x } - \mathrm { z } ) \mathbf { j } + ( \mathrm { z } - \mathrm { x } ) \mathbf { k } ; \mathrm { S } : \mathrm { r } ( \mathrm { r } , \theta ) = \mathrm { r } \cos \theta \mathbf { i } + \mathrm { r } \sin \theta \mathbf { j } + \left( 9 - \mathrm { r } ^ { 2 } \right) \mathbf { k } , 0 \leq \mathrm { r } \leq 3 \text { and } 0 \leq \theta \leq 2 \pi$$

• A) \(- 36 \pi\)
• B) \(36 \pi\)
• C) \(- 18 \pi\)
• D) \(18 \pi\)

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