(A)The Vector Field ${ \vec { F } } = 2 x \vec { i } + 4 y \vec { j } + a z \vec { k }$

question 5

Essay

(a)The vector field ${ \vec { F } } = 2 x \vec { i } + 4 y \vec { j } + a z \vec { k }$ has the property that the flux of $\vec {F }$ through any closed surface is 0.What is the value of the constant a?
(b)The vector field $\vec { G } = ( a y + b z ) \vec { i } + ( 2 x + 4 z ) \vec { j } + ( 4 x + c y ) \vec { k }$ has the property that the circulation of $\vec { G }$ around any closed curve is 0.What are the values of the constants a, b and c?

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Herzberg's Two-Factor Theory

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Satisfier Factor

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