Spheres of charge: 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 electric potential due to a point charge is given by V = kq/r, where k is Coulomb's constant, q is the charge, and r is the distance from the charge.
For a conductive sphere, the excess charge resides on its surface. Thus, the potential due to a conducting sphere at a point outside of it can be calculated as the potential due to a point charge at the center of the sphere with the same charge as the total charge on the sphere. 
Therefore, the potential at a point 12.0 cm from the center of the sphere is:
V = kq/r = (8.99 × 10^9 N ∙ m^2/C^2)(15.0 × 10^-6 C)/(0.2 m + 0.12 m) = 674 kV
The answer is B.

Spheres of Charge: a Conducting Sphere of Radius 20