A conducting sphere of radius 20.0 cm carries an excess charge of +15.0 µC, and no other charges are present. (k = 1/4πε0 = 8.99 × 10⁹ N ∙ m²/C²) The potential (relative to infinity) due to this sphere at a point 12.0 cm from its center is closest to

Question

Quizplus · Accepted Answer

The potential V at a distance r from a point charge Q is given by:

V = kQ/r

For a conducting sphere, assuming the excess charge is uniformly distributed, we can treat the sphere as a point charge located at its center.

Thus, the potential at a distance of 12.0 cm from the center of the sphere is:

V = kQ/(0.12 m + 0.20 m) = kQ/0.32 m

Plugging in the values, we get:

V = (8.99 × 10^9 N·m^2/C^2)(15.0 × 10^-6 C)/0.32 m = 674 kV

Therefore, the closest option is B.

A Conducting Sphere of Radius 20