Two small balls having equal positive charge $Q$ (coulomb) on each are suspended by two insulating strings of equal length $L$ (meter) from a hook fixed to a stand. The whole setup is taken in a satellite to space where there is no gravity (state of weightlessness).

(a) What is the angle between the two strings?

(b) What is the tension in each string?

Suppose we have a large number of identical particles, very small in size. Any two of them at $10 \mathrm{cm}$ separation repel with a force of $3\times {10}^{-10} \mathrm{N}$.

(a) If one of them is at $10 \mathrm{c}\mathrm{m}$ from a group (of very small size) of $n$ others, how strongly do you expect it to be repelled?

(b) Suppose you measure the repulsion and find it as $6\times {10}^{-6} \mathrm{N}$, how many particles are there in the group?

Find the force on a charge $q_1\left(=20 \mathrm{\mu C}\right)$ due to the charge of $q_2\left(=-10 \mathrm{\mu C}\right)$ if the positions of the charges are given as $P\left(1\text{,} -1\text{,} 2\right)$ and $Q\left(-1\text{,} 1\text{,} 1\right)$ (see figure).

Two identical conducting small spheres are placed with their centres $0.3 \mathrm{m}$ apart. One is given a charge of $12.0 \mathrm{nC}$ and the other a charge of $-18.0 \mathrm{nC}$.

(a) Find the electric force exerted by one sphere on the other?

(b) If the spheres are connected by a conducting wire, find the electric force between the two after they attain equilibrium.