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Chapter 4: Q28E (page 778)

A solid conducting sphere has net positive charge and radius R = 0.400 m. At a point 1.20 m from the center of the sphere, the electric potential due to the charge on the sphere is 24.0 V. Assume that V = 0 at an infinite distance from the sphere. What is the electric potential at the center of the sphere?

Short Answer

Expert verified

The electric potential at the center of the sphere is 72.0V.

Step by step solution

01

Potential Energy

The equation gives the potential energy due to the sphere;

V=14ππ0qr

Here, r denotes the distance between the sphere and the point where the potential is measured; it can be inside or outside the sphere.

02

Electric potential at the center of the sphere

The potential is inversely proportional to the distance, as shown by the equation;

V∞1r

The potential at the sphere's center is determined by the radius R, where the potential is constant throughout the sphere. Because the charge q is constant and the term 14π€0is constant, a relationship between the states inside the sphere and the states outside the sphere can be established.

role="math" localid="1664260877266" V1V2=r2r1VinsideVouside=rRVinside=rRVouside

Putting the values;

Vinside=1.2m0.40m24.0V

Hence, the electric potential at the center of the sphere is 72.0V.

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