We would apply the Coulomb's law which states that electric force acting between two charged objects depends directly on the product of the charges and inversely on the square of the distance between them. It is expressed as
F = kq1q2/r^2
where
F is the force between the charges
k is the Coulomb's force constant and its value is 9 x 10^9 N/m^2c^2
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
From the information given,
F = 3.0 x 10⁻⁶ N
r = 10 cm
we would convert from cm to m.
Recall, 100 cm = 1 m
10cm = 10/100 = 0.1 m
By substituting these values into the formula, we have
3.0 x 10^-6 = (9 x 10^9 x q1q2)/0.1^2
By crossmultiplying, we have
3.0 x 10^-6 x 0.1^2 = 9 x 10^9 x q1q2
Dividing both sides of the equation by 9 x 10^9 , we have
q1q2 = (3.0 x 10^-6 x 0.1^2)/9 x 10^9
q1q2 = 333.33 x 10^-20
If the separation is increased to 30 cm, then r = 30 cm. Converting 30 cm to m,
r = 30/100 = 0.3m
Thus,
F = (9 x 10^9 x 333.33 x 10^-20)/0.3^2
F = 3.333 x 10^- 7 N
The force formed by increasing the separation to 30 cm is 3.333 x 10^- 7 N