Charge Q = +8 %u03BCC is distributed uniformly over the volume of a non-conducti
ID: 2122404 • Letter: C
Question
Charge Q = +8 %u03BCC is distributed uniformly over the volume of a non-conducting sphere of radius R= 25 cm.
(a) Calculate the charge density %u03C1 in C/m3. ( 1 %u03BCC = 10-6 C, 1 m = 100 cm.)
(b) For outside (r > R), draw a figure and show your Gaussian surface. What is the
enclosed charge? Use the Gauss%u2019 law to find the magnitude of the E-field as a
function of r. (r is NOT known numerically.)
(c) For inside (r < R), draw a Gaussian surface and calculate the charge enclosed as a
function of r. (No integration is needed!). Now use the Gauss%u2019 law to find the
magnitude of the E-field inside the sphere as a function of r.
(d) Plot (roughly) the E-field as a function of r for inside and outside in the same graph.
Explanation / Answer
Q = 8 micro C
V = (4/3)*pi*0.25^2 = 0.06542 m^3
a)volume charge density, rho = Q/V = 1.223*10^-4 C/m^3
b)when r >R
E = k*Q/r^2
c) at r<R
charge elclosed q = rho*(4/3)*pi*r^3 =(4/3)*pi*r^3 * Q/(4/3 *pi*R^3 )
q = Q*r^3/R^3
Accoring to gauss law E*4*pi*r^2 = q/epsilon
E = Q*r/(4*pi*epsilon*R^3)
d) elecric filed at the center is zero.as we move from center to surface E value increases.
at the E is maximum. and as we move away from the surface E value decreases.