Question

explain what will happen to the electrostatic force between sphere a and b if the distance between them is doubled.

Explanation:

Step1: Recall Coulomb's Law

Coulomb's Law states that \( F = k\frac{q_1q_2}{r^2}\), where \(F\) is the electrostatic force, \(k\) is a constant, \(q_1\) and \(q_2\) are the charges of the two objects, and \(r\) is the distance between them.

Step2: Analyze the effect of doubling the distance

Let the original distance be \(r\) and the original force be \(F_1=k\frac{q_1q_2}{r^2}\). When the distance is doubled (\(r_2 = 2r\)), the new force \(F_2=k\frac{q_1q_2}{(2r)^2}\).
Simplify \(F_2\):

$$
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Since \(F_1 = k\frac{q_1q_2}{r^2}\), we have \(F_2=\frac{1}{4}F_1\).

Answer:

The electrostatic force will be one - fourth of the original value.