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## Homework Statement

An insulated spherical shell with its center in the origin and radius R has a surface charge density of [tex]\sigma(\theta)=\sigma_0\sin(\theta)[/tex] when [tex]\theta[/tex] is the angle from the z axis. Calculate the electrical field outside the shell at point z=R.

## Homework Equations

Gauss's Law

[tex]\int\int{\vec{E}\cdot\vec{dS}}=4\pi{Q_{in}}[/tex]

## The Attempt at a Solution

I tried first calculating the overall charge of the spherical shell:

[tex]Q=R^2\int_0^{2\pi}\sigma_0\sin^2\theta{d\theta}\int_0^\pi{d\phi}=\frac{R^2\sigma_0}{2}\int_0^{2\pi}(1-\cos{2\theta})d\theta\cdot\pi=\frac{1}{2}\pi{R^2}\sigma_0\cdot{2\pi}=\pi^2R^2\sigma_0[/tex]

However, I don't see how Gauss's Law can help me find the electrical field at that specific point.

Please help!