Find the Flux of the Curl of Field F Through $\mathbf { F } = x ^ { 2 } \mathbf { i } + 6 x \mathbf { j } + 9 \mathbf { k } ; \mathrm { S }$

question 54

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $\mathbf { F } = x ^ { 2 } \mathbf { i } + 6 x \mathbf { j } + 9 \mathbf { k } ; \mathrm { S }$ is the upper hemisphere of $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } = 16$

• A) \(16 \pi\)
• B) 16
• C) \(96 \pi\)
• D) \(\pi\)

---

Definitions:

Brainstem Structures

The lower part of the brain that connects the cerebrum with the spinal cord and controls basic life functions such as breathing.

Limbic System

A complex system of nerves and networks in the brain, associated with instincts, moods, and emotions.

Anterior Thalamus

A part of the thalamus located towards the front of the brain, playing a role in relaying sensory information and in the regulation of consciousness and sleep.

Medial Forebrain Bundle

A neural pathway in the brain that connects the brainstem to various structures in the forebrain, involved in the mediation of reward and pleasure.