A nonconducting sphere of radius 10 cm is charged uniformly with a density of 100 nC/m3. What is the magnitude of the potential difference between the center and a point 4.0 cm away? Group of answer choices 12 V 4.7 V 2.2 V 6.8 V 3.0 V

The answer is 3.0 V

Explanation:

the formula of the potential due to a non-conductive sphere with a uniform charge at a point at a distance x from the center of the sphere is equal to:

V1 = (2*π*k*ρ*(3*r^2 - x^2))/3

where

ρ = volume charge density = 100 nC/m^3

x = distance from center = 0

r = radius = 10 cm = 0.1 m

Thus:

V1 = (2*π*k*ρ*3*r^2)/3

for x = 4 cm = 0.04 m, we have:

V4 = (2*π*k*ρ*(3*r^2 - (0.04^2))/3 = (2*π*k*ρ*(3*r^2 - 0.0016))/3

The difference between both equations:

V1 - V4 = (2*π*k*ρ*3*r^2)/3 - (2*π*k*ρ*(3*r^2 - 0.0016))/3

V1 - V4 = (2*π*k*ρ*0.0016)/3 = (2*π*9x10^9*100x10^-9*0.0016)/3 = 3.02 V = 3 V

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