Integrating Vector Fields on a Sphere

[iloveannaw]

Homework Statement

Given two vector fields:
i)
$$A \frac{\vec{r}}{r^{n_{1}}}$$
ii) $$Ae_{z} \times \frac{\vec{r}}{r^{n_{2}}}$$

where A is a constant and $$n_{1} \neq 3$$ and $$n_{2} \neq 2$$

find $$\int \vec{F} dS$$ through surface of a sphere of radius R

Homework Equations

$$\int \vec{F} r^{2} sin(\vartheta) d\vartheta d\varphi$$

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

$$I = 4 \pi A R^{3 - n_{1}}$$

and as for the second
$$Ae_{z} \times \frac{\vec{r}}{r^{n_{2}}}$$

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

with result that integral

$$I = \pi^{2} A R^{3 - n_{2}}$$could someone give me a few pointers, please

thanks

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

 

[fzero]

Do you mean

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

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