Answer : The distance between the cup and metal sphere is 0.1457 meter.
Solution : Given,
Charge on the cup = [tex]2.0\times 10^{-6}coulombs[/tex]
Charge on metal = [tex]2.5\times 10^{-6}coulombs[/tex]
Electric force = 2.12 Newton
coulombs constant, K = [tex]9.0\times 10^9Nm^2/coulombs^2[/tex]
Formula used : According to the Coulombs Law,
[tex]F=K_e\times \frac{q_1q_2}{r^2}[/tex]
where,
F = Electric force
[tex]K_e[/tex] = coulombs constant
[tex]q_1[/tex] = Charge on the cup
[tex]q_2[/tex] = Charge on the metal
r = Distance between the two charged species
Now put all the given values in above formula, we get
[tex]2.12N=9.0\times 10^9Nm^2/coulombs^2\times \frac{(2.0\times 10^{-6}coulombs)\times (2.0\times 10^{-6}coulombs)}{r^2}[/tex]
By rearranging the terms, we get the value of 'r'
r = 0.1457 meter
Therefore, the distance between the cup and metal sphere is 0.1457 meter.
