Gauss Theory (1 Viewer)

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1. The problem statement, all variables and given/known data

Given two vector fields:
[tex]A \frac{\vec{r}}{r^{n_{1}}} [/tex]
ii) [tex]Ae_{z} \times \frac{\vec{r}}{r^{n_{2}}} [/tex]

where A is a constant and [tex]n_{1} \neq 3 [/tex] and [tex]n_{2} \neq 2 [/tex]

find [tex]\int \vec{F} dS[/tex] through surface of a sphere of radius R

2. Relevant equations

[tex]\int \vec{F} r^{2} sin(\vartheta) d\vartheta d\varphi[/tex]

3. The attempt at a solution
heres my attempt at the first field

INTEGRAL A/r^(n_1 - 1) * e_r * r^2 sin(theta) dtheta dfi

[tex] I = 4 \pi A R^{3 - n_{1}} [/tex]

and as for the second
[tex]Ae_{z} \times \frac{\vec{r}}{r^{n_{2}}} [/tex]

A sin(theta) / r^(n_2 - 1) * e_(fi)

with result that integral

[tex] I = \pi^{2} A R^{3 - n_{2}} [/tex]

could someone give me a few pointers, please


ps sorry but latex isn't doing what it's supposed to
Last edited:


Science Advisor
Homework Helper
Gold Member
Do you mean

\int \vec{F}\cdot \hat{n} dS

where [tex]\hat{n}[/tex] is the unit normal to the surface? If so, you should give working out the relevant dot products a shot.

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