Consider two concentric spherical shells, with radius R_1 = 2.0 cm and R_2 = 4.0
ID: 1521051 • Letter: C
Question
Consider two concentric spherical shells, with radius R_1 = 2.0 cm and R_2 = 4.0 cm, uniformly charged, respectively, with surface charges Q_1 = +35.0 x 10^6 C and Q_2= -25.0 x 10^-6 C. Determine the electric field E (r) at a point distant r from the center of the shells for the cases: You can express your results as a function of r. What is the electric force F acting on a charge q = -2.0 nC located at r 5.0 cm away from the center of the shells? Indicate the direction of the force in a schematic diagram.Explanation / Answer
a)
r < R1
consider a gaussian sphere of radius r
the charge inside the gaussian sphere = 0
from gauss law
integration E*ds = qin/eo
E*4*pi*r^2 = 0
E = 0
++++++
b)
R1 < r < R2
consider a gaussian sphere of radius r
the charge inside the gaussian sphere = Q1
from gauss law
integration E*ds = qin/eo
E*4*pi*r^2 = 35*10^-6/(8.84*10^-12)
E = 315069.17/r^2
(c)
r > R2
consider a gaussian sphere of radius r
the charge inside the gaussian sphere = Q1+Q2
from gauss law
integration E*ds = qin/eo
E*4*pi*r^2 = (35-25)*10^-6/(8.84*10^-12)
E = 90019.76/r^2
++++++++++++++++++++++
F = E*q = (90019.76/0.05^2)*2*10^-9 = 0.072015808 N
the force towards the center of the sphere