An unknown charge sits on a conducting solid sphere of radius 10 cm . If the electric field 15 c

step 1 All right, so for this one, you have a sphere with a radius, 10 meters, excuse me, how many cent

An unknown charge sits on a conducting solid sphere of...

An unknown charge sits on a conducting solid sphere of
radius 10 $\mathrm{cm} .$ If the electric field 15 $\mathrm{cm}$ from the center of the
sphere has the magnitude $3.0 \times 10^{3} \mathrm{N} / \mathrm{C}$ and is directed radially in-
ward, what is the net charge on the sphere?

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Key Concepts

Gauss's Law

Gauss's Law states that the net electric flux through a closed surface is proportional to the total charge enclosed by that surface. This relationship allows for the calculation of the net charge on an object when there is symmetry in the electric field, simplifying the analysis of charge distributions.

Spherical Symmetry in Charge Distributions

For spherically symmetric charge distributions, such as those found on a conducting sphere, the electric field outside the sphere behaves identically to that produced by a point charge located at the center. This concept enables the application of the inverse square law for the electric field, E = kQ/r², to determine the net charge from the field measured at a distance.

Conductors in Electrostatics

When dealing with conductors in electrostatic equilibrium, the free charges reside on the surface, resulting in a uniform charge distribution over a spherical conductor. This property ensures that the external electric field is solely determined by the net charge, making the use of Gauss's Law effective in such analyses.

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