Energy Density In Electrostatic Field / Work Done To Assemble Charges.
- In case, if we wish to assemble a number of charges in an empty system, work is required to do so. - Also electrostatic energy is said to be stored in such a collection. - Let us build up a system in which we position three point charges Q 1 , Q 2 and Q 3 at position r 1 , r 2 and r 3 respectively in an initially empty system. - Consider a point charge Q 1 transferred from infinity to position r 1 in the system . It takes no work to bring the first charge from infinity since there is no electric field to fight against (as the system is empty i.e. charge free). Hence, W 1 = 0 J - Now bring in another point charge Q 2 from infinity to position r 2 in the system. In this case we have to do work against the electric field generated by the first charge Q 1 . Hence, W 2 = Q 2 V 21 where V 21 is the electrostatic potential at point r 2 due to Q 1 . - Work done W 2 is also given as: - Now bring in another point charge Q 3 from infinity t...