(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?

Question

(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?

Quizplus · Accepted Answer

The Answer of (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?

(A)The Vector Field F⃗=2xi⃗+4yj⃗+azk⃗ { \vec { F } } = 2 x \vec { i } + 4 y \vec { j } + a z \vec { k }F=2xi+4yj​+azk

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