A nonconducting sphere has radius R 129 cm and uniformly di

A nonconducting sphere has radius R = 1.29 cm and uniformly distributed charge q = +2.36 fC. Take the electric potential at the sphere\'s center to be V0 = 0. What is V at radial distance from the center (a) r = 0.390 cm and (b) r = R? (Hint: See an expression for the electric field.)

Solution

v(r) = -q r² / (8 pi * epsilon₀ * R³)

= -(2.36 * 10^-15 * (0.390 * 10^-2)² ) / (8 pi * epsilon₀ * (1.29 * 10^-2)³)

= -0.0000752 = -7.52 * 10-5 V

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r = R

v(r) = -q / (8 pi * epsilon₀ * R)

= -(2.36 * 10^-15 ) / (8 pi * epsilon₀ * (1.29 * 10^-2))

= -8.22 * 10^-4 V