I am wondering what the set of area vectors for a surface would be. For a plane on the xy-plane, I know the set of area vectors is <0,0,dx*dy>.
So, for a set of points (x,y,z) that make a paraboloid, if F(x,y,z)=0 then [grad(F)•<dy*dz, dx*dz, dx*dy>]/mag(grad(F)) would be the set of area vectors?
(i'm not sure if I'm correct in assuming the area vector needs to be a unit vector)
grad(F) is the gradient of F
mag(grad(F)) is the magnitude of the gradient field of F
The Attempt at a Solution
So for paraboloid x^2+y^2+z=0, the area vectors would be <(2x/sqrt(4x^2+4y^2+1))*dydz, (2y/sqrt(4x^2+4y^2+1))*dxdz, (1/sqrt(4x^2+4y^2+1))*dxdy>
yea, I am very confused. I would like to know this for integrating electric vector fields for flux.