Answer to Question #253876 in Electricity and Magnetism for zuzu

Question

How many excess electrons must be added to a plastic solid sphere that has a diameter of 0.26 m to produce an electric field of 1030 N/C at the edge of the surface? Assuming the charge is uniform, what is the electric field at 10 cm from the center?

Answer 1

Charge

$Q=4\pi\epsilon_0R^2E$

Put value

$$Q=\frac{1030\times0.13^2}{9\times10^9}=\frac{17.407}{9\times10^9}=1.9341\times10^{-9}C$$

Number of electrons

$N=\frac{Q}{1.6\times10^{-19}}$

Put value

$N=\frac{1.9341\times10^{-9}}{1.6\times10^{-19}}=1.20\times10^{10}$

Now electric field inside the sphere

$E_i=\frac{kQr}{R^3}$

$E_i=\frac{9\times10^9\times1.934\times10^{-9}\times0.1}{0.13^3}$

E_i=792.26 N/C