I have come upon a paradox, to me, in the vector characteristics of electric flux. I wonder if others have fallen into - and resolved - this problem and might be able to resolve this.
An electric field is a vector and hence when it contacts, and passes through a surface of area dA, it would seem that it is still a vector, ie. the electric flux dψ in the equation dψ=E n dA (where E and the unit vector n are both vectors) must also be a vector.
When integrated, ψ, is regarded as a scalar. It would seem that the flux ψ must "flow" in a direction and my problem is that it would still seem to have the characteristics of a vector.
Wikipedia states (http://en.wikipedia.org/wiki/Flux)
In the study of transport phenomena (heat transfer, mass transfer and fluid dynamics), flux is defined as the amount that flows through a unit area per unit time. Flux in this definition is a vector.
In the field of electromagnetism and mathematics, flux is usually the integral of a vector quantity over a finite surface. It is an integral operator and acts on a vector field as do the gradient, divergence and curl found in vector analysis. The result of this integration is a scalar quantity.
WHY IS THE INTEGRATED ELECTRIC FLUX NOT A VECTOR?
An electric field is a vector and hence when it contacts, and passes through a surface of area dA, it would seem that it is still a vector, ie. the electric flux dψ in the equation dψ=E n dA (where E and the unit vector n are both vectors) must also be a vector.
When integrated, ψ, is regarded as a scalar. It would seem that the flux ψ must "flow" in a direction and my problem is that it would still seem to have the characteristics of a vector.
Wikipedia states (http://en.wikipedia.org/wiki/Flux)
In the study of transport phenomena (heat transfer, mass transfer and fluid dynamics), flux is defined as the amount that flows through a unit area per unit time. Flux in this definition is a vector.
In the field of electromagnetism and mathematics, flux is usually the integral of a vector quantity over a finite surface. It is an integral operator and acts on a vector field as do the gradient, divergence and curl found in vector analysis. The result of this integration is a scalar quantity.
WHY IS THE INTEGRATED ELECTRIC FLUX NOT A VECTOR?