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 the two charges, we can use Coulomb’s Law, which is given by the formula:

[

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

]

where:

– ( F ) is the force between the charges (0.1 N),

– ( k ) is Coulomb’s constant (( 8.99 times 10^9 , text{Nm}^2/text{C}^2 )),

– ( q_1 ) and ( q_2 ) are the magnitudes of the charges (( 2 times 10^{-7} , C ) and ( 4.5 times 10^{-7} , C ), respectively),

– ( r ) is the distance between the charges.

Rearranging the formula to solve for ( r ) gives:

[

r = sqrt{k frac{|q_1 q_2|}{F}}

]

Now we can substitute the given values into the formula:

[

r = sqrt{8.99 times 10^9 , frac{(2 times 10^{-7})(4.5 times 10^{-7})}{0.1}}

]

Calculating the numerator:

[

|q_1 q_2| = (2 times 10^{-7})(4.5 times 10