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To find the separation between the two charged dielectric balls, we can employ Coulomb’s Law and the equilibrium condition due to the gravitational force acting on the upper ball.
Coulomb’s Law gives us the electrostatic force (F_e) between two charges:
[ F_e = k_e frac{|q_1 q_2|}{r^2} ]
where
– (k_e = 8.99 times 10^9 , text{N}cdottext{m}^2/text{C}^2) is the Coulomb’s constant,
– (q_1) and (q_2) are the charges of the balls, which are each (1 mu C = 1 times 10^{-6} C),
– (r) is the separation between the centers of the two balls, which we are trying to find.
The gravitational force (F_g) acting on the upper ball is given by:
[ F_g = mg ]
where
– (m = 10 , text{gm} = 0.01 , text{kg}) is the mass of the ball,
– (g = 9.8 , text{m/s}^2) is the acceleration due to gravity.
At equilibrium, the electrostatic force of repulsion between the balls is equal to the gravitational force pulling the upper ball downwards:
[ F_e = F_g
c
Explanation: F = mg = 10 X 10-3 X 9.81 = 9.81 X 10-2 N.
On calculating r by substituting charges, we get r = 0.3m