Two identical particles are charged and held at a distance of 1m form each other. They are found to be attraction each other with a force of 0.027N . Now they are connected by a conducting wire so that charge flows between them. When the charge flow stop, they are found to be repelling each other with a force of 0.009N. Find the initial charge on each particle.

Explanation

As both the spheres are attracted to each other , let the charges on both the spheres be `q_1` and `-q_2`. Given , initial force of attraction between both the spheres:
`rArr F=1/(4piepsilon_0)(q_1q_2)/(1)^2` =0.027 N
`rArr q_1q_2=0.027/(9xx10^9)=0.003xx10^(-9)C^2`
When both the spheres are brought in contact , the charge on them is redistributed, thus net charge on each sphere will be `((q_1+(-q_2))/2)`
Force of repulsion between both the spheres will be :
`rArr F.=1/(4piepsilon_0) ((q_1-q_2)/2)^2/(1)^2 =0.009`
`rArr (q_1-q_2)^2/(4xx4piepsilon_0)` =0.009
`(q_1-q_2)^2=(0.009xx4)/(9xx10^9)=4xx10^(-12)`
`q_1-q_2=2xx10^(-6)` ...(i)
Also , `(q_1+q_2)^2=(q_1-q_2)^2+4q_1q_2`
`rArr (q_1+q_2)^2 =4xx10^(-12)+12xx10^(-12)=16xx10^(-12)`
`rArr q_1+q_2=4xx10^(-6)` ....(iii)
From , (i) and (ii) , we get `q_1=3xx10^(-6)` C and `q_2=1xx10^(-6)`C