Find the Flux of the Vector Field F Across the Surface

question 216

Multiple Choice

Find the flux of the vector field F across the surface S in the indicated direction.
- $\mathbf { F } = 5 x \mathbf { i } + 5 y \mathbf { j } + \mathrm { z } ^ { 2 } \mathbf { k } ; \mathrm { S }$ is portion of the cylinder $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } = 25$ between $\mathrm { z } = 0$ and $\mathrm { z } = 5$ ; direction is outward

• A) 625
• B) 1250
• C) \(- 1250 \pi\)
• D) \(1250 \pi\)

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Definitions:

Negative Terminal

The terminal of an electrical device (such as a battery) through which current flows out, typically regarded as the source of electrons.

Cathode

The negative terminal of an electric device.

Lead-acid Batteries

A type of rechargeable battery that uses lead peroxide and sponge lead, employing a sulfuric acid electrolyte.

Electrolyte

A substance that produces an electrically conducting solution when dissolved in a polar solvent, such as water, facilitating the flow of electric charge.