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 A) 0.35 nC. B) 79 nC. C) 315 nC. D) 350 nC. E) 700 nC.

Question

Quizplus · Accepted Answer

We can use the formula for the potential of a conducting sphere:

V = kQ/r

where V is the potential, Q is the charge, r is the radius/diameter of the sphere, and k is Coulomb's constant.

We can rearrange this to solve for Q:

Q = Vr/k

Substituting in the given values:

Q = (14,000 V)(0.225 m)/(8.99 x 10^9 N*m^2/C^2)

Q = 350.4 x 10^-9 C

Rounding to two significant figures, the closest answer choice is D) 350 nC.

A Conducting Sphere 45 Cm in Diameter Carries an Excess