Unravelling Electric Flux: Area Vector and E-Field Vector

[anonymousphys]

1. When solving for electric flux, we dot product the area vector and the e-field vector. Why does area have a vector, and why is it perpendicular to the surface?

Homework Equations

phi=EA

The Attempt at a Solution

Isn't area scalar; Is it because we just want to simplify the calculations so we "imagine" it to be vector?

Thanks for any replies.

 

[tiny-tim]

Welcome to PF!

1. When solving for magnetic flux, we dot product the area vector and the e-field vector. Why does area have a vector, and why is it perpendicular to the surface?
…
Isn't area scalar; Is it because we just want to simplify the calculations so we "imagine" it to be vector?

Hi anonymousphys! Welcome to PF!

Basically for the same reason that to find the angle between two planes, we actually find the angle between their normals.

(Scalar) flux is the amount of a vector field going through a surface.

It's proportional to area, but it also depends on the angle the area presents to the field direction.

Imagine a "tube" of flux … the flux through any surface cutting that tube will be the same, but if the surface is angled, the surface area will be larger by an amount (in the limit) equal to 1/cosine of the angle, so we have to multiply the area by the cosine first to keep the result the same for all angles.

 

[kerimek]

The concept of electric flux is used to describe the flow of electric field through a given surface. In order to calculate this, we use the equation phi=EA, where phi represents the electric flux, E represents the electric field, and A represents the area.

The reason why we consider area to have a vector is because it is not just the magnitude of the area that matters, but also its direction. The direction of the area vector is perpendicular to the surface, which is essential in determining the amount of electric field passing through that surface.

Think of it this way: when we calculate the electric flux, we are essentially measuring the amount of electric field passing through a specific area. The direction of the electric field vector and the direction of the area vector must be perpendicular in order to accurately measure this flux. If the area vector was not perpendicular to the surface, the calculation would not accurately represent the amount of electric field passing through that surface.

Therefore, the area vector is not just a simplification of calculations, but an essential component in accurately determining the electric flux.