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

step 1 In this question, we have a small charge object, spherical charge object, K, carries a charge of

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 $100 \mathrm{~V}$ ? $50.0$ V? $25.0 \mathrm{~V}$ ? Is the spacing of the equipotentials proportional to the change in voltage?

Key Concepts

Electric Potential

Electric potential represents the work done per unit charge in bringing a positive test charge from a reference point (typically infinity) to a specified point in an electric field. For a point charge, this is expressed as V = kQ/r, meaning the potential decreases as the distance from the charge increases.

Equipotential Surfaces

Equipotential surfaces are surfaces on which every point has the same electric potential. In the context of a point charge, these surfaces are spherical shells centered on the charge. Movement along an equipotential requires no work, though distances between different equipotentials vary non-linearly due to the inverse relationship between potential and distance.

Inverse Proportionality in Electrostatics

The relationship between electric potential and distance for a point charge is characterized by an inverse proportionality (1/r). This means that as the distance from the charge increases, the potential decreases at a rate that is not linear, leading to equipotential surfaces that are not evenly spaced for equal differences in voltage.

Coulomb's Constant

Coulomb's constant (k), approximately 8.99×10^9 N·m²/C² in SI units, scales the strength of the electrostatic interaction in equations such as V = kQ/r. It is a fundamental constant that relates the magnitude of charges to the resulting potential and force in an electrostatic field.

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