A hollow metal sphere carries a charge of 6.0 μC . A second hollow metal sphere with a radius th

step 1 There is a hollow metal sphere that carries a charge of six micropoleum. So let us draw the sphe

A hollow metal sphere carries a charge of 6.0 μC . A second...

A hollow metal sphere carries a charge of $6.0 \mu \mathrm{C} . \mathrm{A}$ second hollow metal sphere with a radius that is double the size of the first carries a charge of $18.0 \mu \mathrm{C}$. The two spheres are brought into contact with each other, then separated. How much charge is on each?

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Key Concepts

Influence of Geometry on Electric Potential

The electric potential of a conductor depends on its shape and size. In the case of spherical conductors, the potential is directly proportional to the charge divided by the radius (V = kQ/R). This geometric relationship is crucial in problems where conductors of different sizes share charge, as it affects how the total charge is repartitioned to equalize the potential.

Equalization of Electric Potential in Conductors

When conductors are brought into contact, charge flows between them until they reach the same electric potential. This is a consequence of the fact that any potential difference would cause continued charge movement until equilibrium is attained. For simple geometries like spheres, the potential is related to the charge and the radius, and the equal potential condition ultimately determines the final charge distribution.

Conservation of Charge

This principle states that the total electric charge in an isolated system remains constant. When conductors come into contact, the sum of their charges before contact must equal the sum after they have reached electrostatic equilibrium.

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