Find the Flux of the Curl of Field F Through $\mathbf { F } = ( 4 - \mathrm { y } ) \mathbf { i } + ( 3 + \mathrm { x } ) \mathbf { j } + \mathrm { z } ^ { 5 } \mathbf { k } ; \mathrm { S }$

question 211

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $\mathbf { F } = ( 4 - \mathrm { y } ) \mathbf { i } + ( 3 + \mathrm { x } ) \mathbf { j } + \mathrm { z } ^ { 5 } \mathbf { k } ; \mathrm { S }$ is the upper hemisphere of $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } = 16$

• A) \(64 \pi\)
• B) \(2 \pi\)
• C) \(32 \pi\)
• D) \(- 4 \pi\)

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