Explanation:
Let two charges are
, such that,
.............(1)
Distance between charges, r = 3 m
The force of repulsion between them is, F = 0.075 N
We can consider that both charges are positive, so that there exists the force of repulsion. The force of repulsion is given by :
![F=k\dfrac{q_1q_2}{r^2}](https://tex.z-dn.net/?f=F%3Dk%5Cdfrac%7Bq_1q_2%7D%7Br%5E2%7D)
![q_1q_2=\dfrac{Fr^2}{k}](https://tex.z-dn.net/?f=q_1q_2%3D%5Cdfrac%7BFr%5E2%7D%7Bk%7D)
![q_1q_2=\dfrac{0.075\times 3^2}{9\times 10^9}](https://tex.z-dn.net/?f=q_1q_2%3D%5Cdfrac%7B0.075%5Ctimes%203%5E2%7D%7B9%5Ctimes%2010%5E9%7D)
.............(2)
On solving equation (1) and (2) we get :
![q_1=0.382\ \mu C](https://tex.z-dn.net/?f=q_1%3D0.382%5C%20%5Cmu%20C)
![q_2=19.618\ \mu C](https://tex.z-dn.net/?f=q_2%3D19.618%5C%20%5Cmu%20C)
(b) Now the force of attractive, F = -0.525 N
Let charges are
such that,
.............(3)
Force of attraction is given by :
![F=k\dfrac{q_1q_2}{r^2}](https://tex.z-dn.net/?f=F%3Dk%5Cdfrac%7Bq_1q_2%7D%7Br%5E2%7D)
![q_1q_2=\dfrac{Fr^2}{k}](https://tex.z-dn.net/?f=q_1q_2%3D%5Cdfrac%7BFr%5E2%7D%7Bk%7D)
![q_1q_2=\dfrac{-0.525\times 3^2}{9\times 10^9}](https://tex.z-dn.net/?f=q_1q_2%3D%5Cdfrac%7B-0.525%5Ctimes%203%5E2%7D%7B9%5Ctimes%2010%5E9%7D)
.............(4)
Now on solving equation (3) and (4) we get :
![q_1=0.266\ \mu C](https://tex.z-dn.net/?f=q_1%3D0.266%5C%20%5Cmu%20C)
and
![q_2=-19.734\ \mu C](https://tex.z-dn.net/?f=q_2%3D-19.734%5C%20%5Cmu%20C)
Hence, this is the required solution.