A solid conducting sphere of 9 cm radius has a net charge of 17 nC.If the potential at infinity is taken as zero,what is the potential at the center of the sphere? A) 2.5 μV B) 13.8 μV C) 1.7 × 10³ V D) 1.7 × 10⁴ V E) 9.3 μV

Question

A solid conducting sphere of 9 cm radius has a net charge of 17 nC.If the potential at infinity is taken as zero,what is the potential at the center of the sphere? A) 2.5 μV B) 13.8 μV C) 1.7 × 10³ V D) >1.7 × 10⁴ V E) 9.3 μV

Quizplus · Accepted Answer

The potential at the center of a conducting sphere is given by:

V = kQ/R

where k is Coulomb's constant, Q is the charge on the sphere, and R is the radius of the sphere.

Substituting the given values, we get:

V = (9 × 10^9 Nm^2/C^2)(17 × 10^-9 C)/(9 × 10^-2 m)
  = 1.7 × 10^3 V
  = 1.7 × 10^6 μV
  = 1.7 × 10^10 nV

However, the potential at infinity is taken as zero, which means we need to subtract the potential at infinity from the potential at the center of the sphere to get the actual potential at the center. Since the potential at infinity is zero, the actual potential at the center is:

Vactual = V - 0
        = 1.7 × 10^10 nV

Therefore, the best choice is C, 1.7 × 10^10 nV, which is equivalent to 1.7 × 10^1 μV or 17 μV.

A Solid Conducting Sphere of 9 Cm Radius Has a Net