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