Answer to Question #294531 in Electricity and Magnetism for abel

Question

An insulating sphere of radius 8.0 cm carries a uniform volume charge density

of 500 nC/m^3. What is the electric field in N/C at r = 3.0 cm?

Answer 1

$\rho=\frac{q}{V}$

$\rho=\frac{3\times q}{4\pi r^2}$

$q=\frac{\rho \times4\pi r^2}{3}$

$$q=\frac{500\times10^{-9}\times4\times3.14\times0.08^2}{3}=1.33\times10^{-8}C$$

$$E=\frac{kq}{R^3}r=\frac{9\times10^{9}\times1.33\times10^{-8}}{0.08^3}\times0.03=7.013\times10^3N/C$$