A charge of 2 X 10-7 C is acted upon by a force of 0.1N. Determine the distance to the other charge of 4.5 X 10-7 C, both the charges are in vacuum

To determine the distance between two charges in a vacuum, you would typically use Coulomb’s Law, which is given by the equation:

[ F = k cdot frac{{|q_1 cdot q_2|}}{{r^2}} ]

Where:

– (F) is the force between the charges (in Newtons, N),

– (k) is Coulomb’s constant ((8.987 times 10^9 , text{N} cdot text{m}^2/text{C}^2)),

– (q_1) and (q_2) are the magnitudes of the two charges (in Coulombs, C),

– (r) is the distance between the centers of the two charges (in meters, m).

Given:

– (q_1 = 2 times 10^{-7} , text{C}),

– (q_2 = 4.5 times 10^{-7} , text{C}),

– (F = 0.1 , text{N}).

Substitute the given values into Coulomb’s Law and solve for (r):

[ 0.1 = (8.987 times 10^9) cdot frac{{|2 times 10^{-7} cdot 4.5 times 10^{-7}|}}{{r^2}} ]

First,