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Chapter 22: Problem 12

A solid sphere contains positive charge uniformly distributed throughout its volume. Is the potential at its center higher than, lower than, or the same as at the surface?

Short Answer

Expert verified
The potential at the center of the sphere is lower than the potential at the surface.

Step by step solution

01

Calculate potential at the center

Substitute \( r = 0 \) into the formula of potential, which gives \( V_{center} = \frac{kQ}{2R^3}(3R^2-0^2) = \frac{3kQ}{2R} \).
02

Calculate potential at the surface

Substitute \( r = R \) into the formula of potential, which gives \( V_{surface} = \frac{kQ}{2R^3}(3R^2-R^2) = \frac{kQ}{R} \).
03

Compare the potential at the center and the surface

Since \( \frac{3kQ}{2R} < \frac{kQ}{R} \), it can be concluded that the potential at the center of the sphere is lower than the potential at the surface.

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