Flux through sphere NOT centred at origin

[sandy.bridge]

Homework Statement

Let's say the sphere has a radius of 3 and is centred at (3, 0, 3). Is there a way to implement spherical cooridnates, or is it essentially impossible for this situation to not get messy? I have searched everywhere as to how I can evaluate this, but to no avail. Any help is greatly appreciated.

 

[LCKurtz]

Homework Statement

Let's say the sphere has a radius of 3 and is centred at (3, 0, 3). Is there a way to implement spherical cooridnates, or is it essentially impossible for this situation to not get messy? I have searched everywhere as to how I can evaluate this, but to no avail. Any help is greatly appreciated.

Try translating the origin. If the sphere is centered at (a,b,c) try$$
x = a+\rho \sin \phi \cos\theta$$ $$
y = b +\rho \sin \phi \cos\theta$$ $$
z = c +\rho\cos\phi$$This will give you the usual formua for $d\vec S$. $\rho$ would be the constant radius of the sphere.