Answer to Question #314331 in Electricity and Magnetism for Ellie

Question

Two small charged metal spheres are placed 20cm apart in air. If they have +20 x 10^-6 C and +4 x 10^-6 C charges on them respectively, what force acts on them? What is the electric field intensity halfway between them?

Answer 1

The force between charges

$$F=k\frac{Q_1Q_2}{r^2}=9*10^9*\frac{20*10^{-6}*4*10^{-6}}{0.2^2}=18\:\rm N$$

The electric field intensity halfway between charges

$$E=E_1-E_2=k\frac{Q_1}{r^2/4}-k\frac{Q_2}{r^2/4}$$

$$E=9*10^9*\frac{20*10^{-6}}{0.1^2}-9*10^9*\frac{4*10^{-6}}{0.1^2}\\ =1.44*10^7\:\rm N/C$$