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To find the force between two charges, we can use Coulomb’s Law, which is expressed as:
[F = k cdot frac{|q_1 cdot q_2|}{r^2}]
where:
– (F) is the force between the charges,
– (k) is Coulomb’s constant ((8.987 times 10^9 N m^2/C^2)),
– (q_1) and (q_2) are the magnitudes of the two charges (in this case, 2nC and -1nC, which are (2 times 10^{-9}C) and (-1 times 10^{-9}C) respectively),
– and (r) is the distance between the charges (4cm, which needs to be converted to meters, so (r = 0.04 m)).
Substituting the given values:
[F = 8.987 times 10^9 N m^2/C^2 cdot frac{(2 times 10^{-9} C) cdot (1 times 10^{-9} C)}{(0.04 m)^2}]
[F = 8.987 times 10^9 cdot frac{2 times 10^{-18}}{0.0016}]
[F = 8.987 times 10^9 cdot 1.
c
Explanation: Before the charges are brought into contact, F = 11.234 μN.
After charges are brought into contact and then separated, charge on each sphere is,
(q1 + q2)/2 = 0.5nC
On calculating the force with q1 = q2 = 0.5nC, F = 1.404μN