Use Stokes' Theorem to Calculate the Circulation of the Field $\mathbf { F } = 2 \mathrm { y } \mathbf { i } + 8 x \mathbf { j } + \mathrm { z } ^ { 3 } \mathbf { k } ; \mathrm { C } :$

question 109

Multiple Choice

Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction.
- $\mathbf { F } = 2 \mathrm { y } \mathbf { i } + 8 x \mathbf { j } + \mathrm { z } ^ { 3 } \mathbf { k } ; \mathrm { C } :$ the counterclockwise path around the perimeter of the triangle in the $x - y$ plane formed from the $x$ -axis, $y$ -axis, and the line $y = 5 - 4 x$

• A) \(\frac { 75 } { 2 }\)
• B) \(\frac { 15 } { 4 }\)
• C) \(- \frac { 75 } { 2 }\)
• D) \(\frac { 75 } { 4 }\)

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Definitions:

Action Potentials

Brief reversals in the electrical charge of a neuron's membrane, which propagate along the neuron to transmit signals.

Neurilemma

The outermost layer of Schwann cells that surrounds the axon of a neuron, essential for the regeneration of peripheral nerve fibers.

Nissl Bodies

Structures found in nerve cells, involved in protein synthesis and recognized by their dark staining with basic dyes.

Ependymal Cells

Glial cells lining the ventricles in the brain and the central canal of the spinal column, involved in producing cerebrospinal fluid.