why like charges repel each other?explain in terms of electrostatics

Two electrons will tend to repel each other because both have a negative electrical charge. Two protons will also tend to repel each other because they both have a positive charge. On the other hand, electrons and protons will be attracted to each other because of their unlike charges.

Since the electron is much smaller and lighter than a proton, when they are attracted to each other due to their unlike charges, the electron usually does most of the moving. This is because the protons have more mass and are harder to get moving. Although electrons are very small, their negative electrical charges are still quite strong. Remember, the negative charge of an electron is the same as the positive electrical charge of the much larger in size proton. This way the atom stays electrically balanced. 

Another important fact about the electrical charges of protons and electrons is that the farther away they are from each other, the less force their electric fields have on each other. Similarly, the closer they are to each other, the more force they will experience from each other due to this invisible force field called an electric field.