sandy.bridge said: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.
The flux through a sphere not centered at the origin is the measure of the flow of a vector field through the surface of the sphere. It takes into account the distance of the sphere from the origin, as well as the direction and magnitude of the vector field at each point on the surface of the sphere.
The flux through a sphere not centered at the origin is calculated using the surface integral formula: Φ = ∫∫S F · dS, where Φ is the flux, F is the vector field, and dS is the differential surface element. This formula takes into account the vector field and the orientation of the surface.
The flux through a sphere not centered at the origin is affected by the distance of the sphere from the origin, the direction and magnitude of the vector field, and the orientation of the surface. It is also affected by the shape and size of the sphere, as well as any obstacles or boundaries within the vector field.
The direction of the vector field at each point on the surface of the sphere affects the flux by determining whether the vector field is flowing into or out of the sphere. If the vector field is flowing in the same direction as the normal vector of the surface, the flux will be positive. If the vector field is flowing in the opposite direction, the flux will be negative.
Yes, the flux through a sphere not centered at the origin can be negative. This occurs when the vector field is flowing in the opposite direction of the normal vector of the surface. In this case, the flux is considered to be entering the surface instead of exiting it, resulting in a negative value.