Two point charges `q_1 and q_2` are 3 m apart and their combined charge is 20 pic. If one repels the other with a force of 0.075 N, what are the two charges ?

Explanation

We have two charges `q_1 and q_2`
r = 3m
`q_1+q_2 = 2muC=20 xx10^(-6)C`
`F =0.075 N`
`F=1/(4piin_0).(q_1q_2)/(r^2)`
`0.075= 9 xx10^(9) xx(q_1q_2)/((3)^2)`
`q_1q_2=0.075 xx10^(-9)`
`q_1q_2=75 xx10^(-12)`
Now we know that
`(q_1-q_2)^2=(q_1+q_2)^2-4q_1q_2`
`(q_1-q_2)^2= (20 xx10^(-6))^2-4 (75 xx10^(-12))`
`=400xx10^(-12) - 300 xx10^(-12)`
`= (400 - 300)xx10^(-12)`
`(q_1-q_2)^2=100xx10^(-12)`
`q_1-q_2=10xx10^(-6)C = 10muC " "...(1)`
and `q_1+q_2=20muC" "...(2)`
Add equations (1) and (2)
`2q_1 =30`
`q_1 = 15 muC`
Put it in (2)
`15+q_2=20`
`q_2=5muC`