# Two point charges of ( +2 mu C ) and ( +6 mu C ) repel each other with a force of ( 12 mathrm{N} ). If each is given an additional charge of ( -4 mu C ), then force will become:-

(1) ( 4 mathrm{N} ) (attractive)

(2) ( 60 mathrm{N} ) (attractive)

(3) ( 4 mathrm{N} ) (repulsive)

(4) ( 12 mathrm{N} ) (attractive)

We know that the force between two charges is given by coloumbs law:

( F=frac{1}{4 pi epsilon_{0}} frac{q_{1} q_{2}}{r^{2}} )

Given that ( F=12 mathrm{N}, mathrm{q}_{1}=2 times 10^{-6} mathrm{C}, mathrm{q}_{2}=6 times 10^{-6} mathrm{C} )

( F=frac{1}{4 pi epsilon_{0}} frac{left(2 times 10^{-6}right) timesleft(6 times 10^{-6}right)}{r^{2}} )

( 12=9 times 10^{9} times frac{left(2 times 10^{-6}right) timesleft(6 times 10^{-6}right)}{r^{2}} )

( r^{2}=9 times 10^{-3} )

When an additional charge is given the force will be:

( F=frac{1}{4 pi epsilon_{0}} frac{left(2-4 times 10^{-6}right) timesleft(6-4 times 10^{-6}right)}{r^{2}} )

( F=9 times 10^{9} times frac{left(-2 times 10^{-6}right) timesleft(2 times 10^{-6}right)}{9 times 10^{-3}} )

( F=-4 N )

Therefore the new force ( =-4 mathrm{N} )