why like charges repel

Hope this helps you,

Every system has a tendency to lower it''s energy.

For a system of 2 like/unlike charges (q1,q2), the energy of the system is given by the equation
U=k(q1)(q2)/r
where U=potential energy
k=constant for a medium(medium is one in which charges are kept eg air, water etc.)
q1,q2=charges(including their sign, positive or negetive)
r=dist. between charges
For U to be minimum, r should be maximum, everything else kept constant.
therefore, like charges move away to increase r.

Incase of unlike charges one will be negetive and other positive. Let q1 be negetive, so U=k(-q1)(q2)/r
Now, for U to be minimum, r should be minimum so charges attract.
Hence like charges repel and unlike attract.

Dear Parvez,

it is worth noting that positive charges have lines of forces moving out from them and negative charges have lines of forces entering them.for attraction of charges one charge must have force line leaving and the other entering,hence they must be opp.
like charges will repel on the otherr side since both the charges will have the same type of lines of forces and will not enter or leave the mutual system of charges at the same time.
it is alo worth mentioning that closer the lines of forces stronger is the charge.the force lines are much like the magnetic field lines but they exist indepenently.also,FORCE LINES DO NOT HAVE PRACTICAL EXISTENCE.

Regards.

due to their magnetic  fielsds the y create around them