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- Homework Statement
- Vector field [itex] F = \begin{pmatrix} x^2 \\ 2y^2 \\ 3z \end{pmatrix} [/itex] has net out flux of [itex] 4 \pi [/itex] for a unit sphere centred at the origin. If we are now given a vector field [itex] F_1 = \begin{pmatrix} x^2 \\ 2y^2 \\ 3(z+1) \end{pmatrix} [/itex], then how does the net out flux compare if we consider a unit sphere centred at (1,0,0) - is it bigger or smaller?

- Relevant Equations
- Gauss' Theorem

Hi,

I just have a quick question about a problem involving Gauss' Theorem.

This is the final part of the question and is worth very few marks, suggesting that I shouldn't need to do any calculations, but I am having trouble arriving at an answer intuitively. The whole question has been about Gauss' Law.

I am stuck and do not know what else to do beyond the realisation that [itex] \nabla \cdot \vec F_1 = \nabla \cdot \vec F [/itex].

Other initial thoughts that I have include:

- This sphere is completely in the +ve regions of the x-axis

- Some points of interest are on the surface of the new sphere: (0,0,0) and (x,y,z=-1)

I would appreciate any help.

Kind regards

I just have a quick question about a problem involving Gauss' Theorem.

**Question:**Vector field [itex] F = \begin{pmatrix} x^2 \\ 2y^2 \\ 3z \end{pmatrix} [/itex] has net out flux of [itex] 4 \pi [/itex] for a unit sphere centred at the origin (calculated in earlier part of question). If we are now given a vector field [itex] F_1 = \begin{pmatrix} x^2 \\ 2y^2 \\ 3(z+1) \end{pmatrix} [/itex], then how does the net out flux compare if we consider a unit sphere centred at (1,0,0) -**is it bigger or smaller (than the 4 [itex] \pi [/itex] calculated earlier)?**This is the final part of the question and is worth very few marks, suggesting that I shouldn't need to do any calculations, but I am having trouble arriving at an answer intuitively. The whole question has been about Gauss' Law.

**Method:**I am stuck and do not know what else to do beyond the realisation that [itex] \nabla \cdot \vec F_1 = \nabla \cdot \vec F [/itex].

Other initial thoughts that I have include:

- This sphere is completely in the +ve regions of the x-axis

- Some points of interest are on the surface of the new sphere: (0,0,0) and (x,y,z=-1)

I would appreciate any help.

Kind regards