Question

Flux

Answer 1

Find a flux of the vector field \[\vec F(x,y,z) = \frac{ m \vec r }{ |\vec r|^3 }\], where m = constant. \[\vec r = x \vec i + y \vec j + z \vec k\] out of a sphere od radius 1 centred at origin.

Answer 2

Don't really remember how to do this, so thought I'd ask for some help, I believe if F is a continuous vector field defined on an oriented surface S with a normal vector n, then the surface integral of F over S is \[\int\limits \int\limits_S \vec F \cdot d \vec S = \int\limits \int\limits \vec F \cdot \vec n dS\]

Answer 3

@Empty @ganeshie8

Answer 4

So I guess \[x^2+y^2+z^2=1\] then we can use a parametric representation?

Answer 5

I think the troubling part is when we cross multiply, not really sure how to visualize it and what way it should be

Answer 6

use a Gaussian surface as it's totally symmetrical

or stuff it into spherical if you want a slightly harder time

Answer 7

Hmm interesting, never really worked with gaussian surfaces, I will look into it, thanks @IrishBoy123

Answer 8

that's what you do anyway
start from cube then use the same for curved