A conducting sphere 45 cm in diameter carries an excess of charge, and no other charges are present. You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The excess charge on this sphere is closest to

Question

Quizplus · Accepted Answer

The potential of a conducting sphere carrying a charge Q can be found using the formula:

V = kQ/R

where k is the Coulomb constant, Q is the charge on the sphere, and R is the radius of the sphere. If we assume that the potential at infinity is zero, then we can find the charge on the sphere as follows:

Q = RV/k

Substituting the given values, we get:

Q = (0.225 m)(14 × 10^3 V) / (8.99 × 10^9 N m^2/C^2)

Simplifying, we get:

Q = 0.0035 C = 3.5 × 10^-3 C

Therefore, the excess charge on the sphere is closest to 350 nC, which is option D.

A Conducting Sphere 45 Cm in Diameter Carries an Excess