An infinitely long solid insulating cylinder of radius a = 3.9 cm is positioned
ID: 1436441 • Letter: A
Question
An infinitely long solid insulating cylinder of radius a = 3.9 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density = 46 C/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 13.1 cm, and outer radius c = 16.1 cm. The conducting shell has a linear charge density = -0.58C/m
3)
What is V(c) - V(a), the potentital difference between the outer surface of the conductor and the outer surface of the insulator?
Explanation / Answer
Use Gauss' Law to find the E-field in the space between the two cylinders. I believe it is;
E = pa^2/2eor , eo=dielectric cnst., p=43x10^-6 C/m3.
Then integrate from r=a to r=b to find;
we are given
a =3.9 cm
= 46 C/m3.
b = 13.1 cm,
c = 16.1 cm.
= -0.58C/m
V(b) - V(a) = -INT[Edr] , r=a to b
=> 13.1-3.9 =9.2
Since in electrostatics all points of a conductor are at the same potential it follows that V(c)=V(b) and therefore;
V(c) - V(a) = -INT[Edr] , r=a to b
=> 16.1 -13.1 =3
The charge on the conducting cylinder is only relevant in preserving the cylindrical symmetry (necessary to use