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.