1) 2) What is V(P) An infinitely long solid insulating cylinder of radius a = 4.
ID: 2137495 • Letter: 1
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1)
2)
What is V(P)
An infinitely long solid insulating cylinder of radius a = 4.6 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density p = 30 uC/m^3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 10.3 cm, and outer radius c = 12.3 cm. The conducting shell has a linear charge density lambda= -0.32uC/m. What is Ey(R), the y-component of the electric field at point R, located a distance d = 51 cm from the origin along the y-axis as shown? What is V(c) - V(a), the potentital difference between the outer surface of the conductor and the outer surface of the insulator? Defining the zero of potential to be along the z-axis (x = y = 0), what is the sign of the potential at the surface of the insulator? V(a) 0 The charge density of the insulating cylinder is now changed to a new value, ?' and it is found that the electric field at point P is now zero. What is the value of ?'?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;
V(b) - V(a) = -INT[Edr] , r=a to b
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
The charge on the conducting cylinder is only relevant in preserving the cylindrical symmetry (necessary to use Gauss' Law) but is otherwise immaterial.
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