Question

Determine the total charge within the sphere r=5m if the charge volume density is (200/(r^2 theta)

Answer 1

In spherical coordinates the total charge within the sphere will be

$$Q=\intop_V\rho_v \text{d}V=$$ $$=\intop^5_{r=0}\space\space\intop^\pi_{\theta=0}\space\space\intop^{2\pi}_{\phi=0} \Big(\frac{200}{r^2\theta}\Big)r^2\text{sin}\theta\space\text{d}r\space\text{d}\theta\space\text{d}\phi=$$

$$=2000\pi\space\text{Si}(\pi)=11636\text{ C}.$$