In: Physics
A charge of uniform linear density 2.20 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 4.00 cm, outer radius = 9.00 cm). The net charge on the shell is zero. (a) What is the magnitude of the electric field at distance r = 13.0 cm from the axis of the shell? What is the surface charge density on the (b) inner and (c) outer surface of the shell?
The expression for calculating the electric flux through a closed surface is calculated as follows:
= E.ds
Here, E is the magnitude of electric field and ds is the surface area of the spherical surface.
the flux through the linear charge rod is calculated as follows:
= Eds
= E x 2pi*r*l
from gauss law
= Q/eo
= l / eo
The expression for calculating the magnitude of electric field by using Gauss’s law is as follows
= E x 2pi*r*l
E = / 2pi*r*eo
E = (2.20 x 10^-9) / (2pi x 0.13 x 8.854 x 10^-12)
E = 304.35 N/C
b)
in = - / 2pi*r
in = -(2.20 x 10^-9) / (2pi x 0.04)
in = -8.75 x 10^-9 C/m^2
c)
out = / 2pi*r
out = (2.20 x 10^-9) / (2pi x 0.09)
out = 3.89 x 10^-9 C/m^2
Here, l is the length of the rod.