Chapter 2.1, Problem 2.7P

Find the electric field a distance z from the center of a spherical surfaceof radius R (Fig. 2.11) that carries a uniform charge density $\sigma$ . Treat the case $z<R$ (inside) as well as $z>R$ (outside). Express your answers in terms of the total chargeq on the sphere. [Hint: Use the law of cosines to write in terms of R and $\theta$ . Be sure to take the positive square root: $\sqrt{R^2+z^2-2Rz}=\left(R-z\right)$ if $R>z$ , but it’s $\left(z-R\right)$ if $R<z$ .]