Find the Flux Of ${ \vec { F } } = x \vec { i } + y \vec { j } + 8 z \vec { k }$

question 33

Multiple Choice

Find the flux of ${ \vec { F } } = x \vec { i } + y \vec { j } + 8 z \vec { k }$ over the sphere S_a, $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = a ^ { 2 }$ , oriented outward, with a > 0.

• A) \(\frac { 40 } { 3 } a ^ { 3 } \pi\)
• B) \(40 a ^ { 3 }\)
• C) \(\frac { 40 } { 3 } a ^ { 2 } \pi\)
• D) \(\frac { 40 } { 3 } a ^ { 3 }\)

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Definitions:

Mumford

Likely referring to an individual or concept in a specific context, without additional information, a precise definition cannot be provided. However, it could relate to leadership studies, particularly the skills model of leadership proposed by Michael Mumford.

Effective Human Leadership Skills

Competencies and qualities that enable an individual to lead others in a way that is productive, empathetic, and inspiring.

Military Structure

The hierarchical organization of armed forces, characterized by strict discipline, clear ranks, and a chain of command.

Katz's Work

Refers to Robert L. Katz's theory that effective leadership depends on three basic personal skills: technical, human, and conceptual.