Spheres of charge: 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 electric potential at the surface of a conducting sphere is given by:

V = kQ/R

Where V is the potential, Q is the charge, R is the radius (which is 22.5 cm in this case), and k is the Coulomb constant.

We can rearrange this equation to solve for the charge Q:

Q = VR/kR

Plugging in the given values, we get:

Q = (14 kV)(0.225 m)/(8.99 × 10^9 N ∙ m^2/C^2)(0.5)

Q ≈ 3.5 × 10^-7 C ≈ 350 nC

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

Spheres of Charge: a Conducting Sphere 45 Cm in Diameter