Question

An insulating sphere is 8.50cm in diameter and carries a 5.85uC charge uniformly distributed throughout its interior volume. Calculate the charge enclosed by a concentric spherical surface with radius r = 2.16cm

Answer 1

The charge enclosed by a concentric spherical surface with radius r = 2.16 cm can be found by volume it takes:

$$v=\frac43\pi r^3.$$

The volumetric charge density is

$$\rho=\frac{Q}{V}=\frac{3Q}{4\pi R^3}.$$

Then the charge within v will be

$$q=\rho v=\frac{3Q}{4\pi R^3}\cdot\frac43\pi r^3=Q\frac{r^3}{R^3}=96\text{ nC}.$$