Explanation:
It is given that,
Let q₁ and q₂ are two small positively charged spheres such that,
[tex]q_1+q_2=5\times 10^{-5}\ C[/tex].............(1)
Force of repulsion between the spheres, F = 1 N
Distance between spheres, d = 2 m
We need to find the charge on the sphere with the smaller charge. The force is given by :
[tex]F=k\dfrac{q_1q_2}{d^2}[/tex]
[tex]q_1q_2=\dfrac{F.d^2}{k}[/tex]
[tex]q_1q_2=\dfrac{1\ N\times (2\ m)^2}{9\times 10^9}[/tex]
[tex]q_1q_2=4.45\times 10^{-10}\ C[/tex]............(2)
On solving the system of equation (1) and (2) using graph we get,
[tex]q_1=0.0000384\ C=38.4\ \mu C[/tex]
[tex]q_2=0.0000116\ C=11.6\ \mu C[/tex]
So, the charge on the smaller sphere is 11.6 micro coulombs. Hence, this is the required solution.
