Charge Q is distributed uniformly throughout the volume of an insulating sphere
ID: 1421722 • Letter: C
Question
Charge Q is distributed uniformly throughout the volume of an insulating sphere of radius R = 4.00 cm. At a distance of r = 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude 790 N/C What is the volume charge density for the sphere? Express your answer to two significant figures and include the appropriate units. What is the magnitude of the electric field at a distance of 2.00 cm from the sphere's center? Express your answer to two significant figures and include the appropriate units.Explanation / Answer
a) r = 8cm is outside the sphere.
so field at this point will be
E = kQ / r^2
790 = (9 x 10^9 x Q) / 0.08^2
Q = 5.62 x 10^-10 C
charge density , rho = Q / (4pi R^3 / 3)
= (5.62 x 10^-10 ) / (4 x pi x 0.04^3 / 3)
= 2.10 x 10^-6 C / m^3 ........Ans
B) using Gauss Law (taking spherical shell as gaussian surface)
total flux = E.A = Qinside / e0
E ( 4 pi r^2) = (rho x 4 pi r^3 / 3 ) / e0
E = (rho x r ) / 3e0 = (2.10 x 10^-6 x 0.02 ) / (3 x 8.854 x 10^-12)
E = 1581.21 N/C