Charge of uniform density rho = +3.4 mu C/m^3 fills a nonconducting solid sphere

Question

Charge of uniform density rho = +3.4 mu C/m^3 fills a nonconducting solid sphere of radius R = 5.1 cm. a.) Electric field: Find the electric field at the following locations, listed in order of decreasing distance: E(r = 6.12 cm) = 0 N/C r E(r = R) = 16531.073 N/C f E(r = 3.5 cm) = 4482.109 N/C ? E(r = 0 cm) = 0 N/C Also, sketch E_r vs. r from r=0 to infinity. On your graph, mark off where r=R occurs. Inside the sphere (r R), graph's shape is: b.) Voltage: Setting V=0 at r = infinity, find the voltage at these same locations. V(r = 6.12 cm) = V(r = R) = 600000 V(r = 3.5 cm) = V(r = 0 cm) Also, sketch V vs. r from r=0 to infinity. On your graph, mark off where r=R occurs. Inside the sphere (r

Explanation / Answer

if r > R

E = KQ/R^2

Q = charge density * volume

volume = 4*pi*r^3/3

r = 5.1 cm = 5.1 x 10^-2 m

Q = 1.889 x 10^-9 C

E = 4539.6 N/C

part b )

if r > R

V = kQ/r

r = 6.12 cm

V = 277.79 V

r = R

V = kQ/R

V = 333.35 V

r < R

V = kQ/2R * ( 3 - r^2/R^2)

r = 3.5 cm

R = 5.1 cm

V = 421.53 V

r = 0

V = 3kQ/2R

V = 500V

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