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The electrostatic force is a fundamental concept in physics that describes the attraction or repulsion between charged objects. When two objects have opposite charges, they attract each other. If they have the same charge, they repel one another. This force is described by Coulomb's Law, which can be mathematically expressed as:\[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \] where:

• \( F \) is the magnitude of the force.
• \( k \) is Coulomb's constant, approximately equal to \( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \).
• \( q_1 \) and \( q_2 \) are the charges involved.
• \( r \) is the distance between the centers of the two charges.

The electrostatic force is crucial in understanding a wide range of phenomena, from how electrons interact at the atomic level to how charged particles behave in electric fields.

Charge redistribution occurs when two conductive objects are brought into contact and charges move to distribute themselves more evenly between the objects.In our exercise, two identical spheres are considered. One sphere initially has a charge of \(+10 \mu \text{C}\) and the other \(-90 \mu \text{C}\).Upon contact, the total charge becomes shared equally because the two spheres are identical in size and shape. The initial total charge is calculated as:\[ +10 \mu \text{C} + (-90 \mu \text{C}) = -80 \mu \text{C} \]After contact, the charge equally distributes, so each sphere ends up with:\[ \frac{-80 \mu \text{C}}{2} = -40 \mu \text{C} \]This redistribution is important as it fundamentally changes how these spheres interact electrostatically when separated again.

Identical spheres in physics problems like this one mean the spheres are similar in size, shape, and material. This is significant because it ensures that when they come into contact, they can redistribute charge equally. The characteristics of identical spheres guarantee that the charge division is even, which simplifies calculations of the subsequent forces between them. After contact, when the spheres are separated at the same distance, identical spheres with uniform charge properties behave consistently under electrostatic principles. This avoids complications that would arise if the spheres differed in size, shape, or material, which might lead to uneven charge distribution.

After charge redistribution, if the spheres are separated by the original distance, the new force can be calculated using Coulomb's Law again. The scenario starts with spheres having charges of \(-40 \mu \text{C}\) each.Applying Coulomb's Law:\[ F' = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \]With both spheres now having the same charge magnitude of \(-40 \mu \text{C}\):\[ F' = k \cdot \frac{-40 \mu \text{C} \cdot -40 \mu \text{C}}{r^2} \]Initially, the force was \( F = k \cdot \frac{10 \mu \text{C} \cdot 90 \mu \text{C}}{r^2} \). The comparison of new and initial forces is the ratio:\[ \frac{F'}{F} = \frac{1600}{900} = \frac{16}{9} \]Thus, the new force is \( \frac{16}{9} \, F \). This shows how charge redistribution changes the interaction significantly.