A small spherical object carries a charge of 8.00 nC . At what distance from the center of the o

step 1 a small spherical object carrying a charge. So this is a small spherical object having the charg

A small spherical object carries a charge of 8.00 nC . At...

A small spherical object carries a charge of 8.00 $\mathrm{nC}$ . At what distance from the center of the object is the potential equal to 100 $\mathrm{V}$ ? 50.0 $\mathrm{V} ? 25.0 \mathrm{V}$ ? Is the spacing of the equipotentials proportional to the change in potential?

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Key Concepts

Electric Potential Due to a Point Charge

The electric potential created by a point charge is given by the formula V = kQ/r, where V is the potential, k is Coulomb's constant, Q is the charge, and r is the distance from the charge. This relationship shows that the potential decreases inversely with distance, which is essential for determining at what distances certain potential values occur around a charged spherical object.

Equipotential Surfaces

Equipotential surfaces are imaginary surfaces on which every point has the same electric potential. For a point charge or small spherical charge distribution, these surfaces form spheres centered on the charge. Understanding equipotentials is important because they help visualize electric fields and indicate that no work is done when moving a charge along an equipotential surface.

Inverse Relationship Between Potential and Distance

Because the potential from a point charge is inversely proportional to the distance, small changes in distance can result in significant changes in the potential near the charge, while farther away the same change in potential corresponds to a larger distance change. This inverse relationship implies that the spacing between equipotential surfaces is not proportional to the change in potential; the surfaces become more widely spaced as one moves away from the charge.

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