Two otherwise identical conducting spheres carry charges of +5.0 μC and -1.0 μC . They are initi

step 1 Here, the net charge is 5 microculum minus 1 microculum equals 4 microculum and after they are b

Two otherwise identical conducting spheres carry charges of...

Two otherwise identical conducting spheres carry charges of $+5.0 \mu \mathrm{C}$ and $-1.0 \mu \mathrm{C} .$ They are initially a large distance $L$ apart. The spheres are brought together, touched together, and then returned to their original separation $L$. What is the ratio of the magnitude of the force on either sphere after they are touched to that before they were touched?

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Key Concepts

Coulomb's Law

Coulomb's Law describes how the electrostatic force between two point charges depends on the magnitude of the charges and the distance between them. Specifically, the force is proportional to the product of the charges and inversely proportional to the square of the distance separating them. This principle is essential for understanding how changes in the charge values (after redistributing through contact) affect the magnitude of the force between the spheres.

Charge Redistribution in Conducting Spheres

When two identical conducting spheres are brought into contact, they share their total charge equally due to the conductive property that allows free movement of charge. This process results in each sphere having an equal share of the combined charge. Recognizing that the spheres are identical simplifies the analysis and is crucial for determining the new charges on the spheres after contact.

Conservation of Charge

The law of conservation of charge states that the total electric charge remains constant in an isolated system. In scenarios where two charged objects come into contact, the sum of their charges before contact is equal to the sum after they redistribute. This principle is fundamental in calculating the new equilibrated charges, which then affects the force between the spheres according to Coulomb's Law.

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