An infinitely long solid insulating cylinder of radius a = 3.8 cm is positioned
ID: 2224620 • Letter: A
Question
An infinitely long solid insulating cylinder of radius a = 3.8 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ? = 26.0 ?C/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 19.7 cm, and outer radius c = 23.7 cm. The conducting shell has a linear charge density ? = -0.39?C/m.
1) What is Ey(R), the y-component of the electric field at point R, located a distance d = 44.0 cm from the origin along the y-axis as shown?
What is V(P)
Explanation / Answer
Use Gauss's Law. Gauss's Law says that the flux of the electric field through a closed surface is directly proportional to the charge enclosed by the surface. I don't know what system of units you're using. In SI, this would be written as: (Flux) = Q / e0 Now, the art of applying Gauss's law is in choosing the right surface. Suppose we have a cylinder centered on the z axis with radius 44 cm and height h. All you have to do is calculate the charge in that surface. It will be something like ?h + V? where V is the volume of the inner cylinder. Apply Gauss's Law to find the flux through the surface. Because of the symmetry of the problem, no flux escapes the top and bottom of the cylinder, and the flux through the outside is constant and is equal to the electric field there multiplied by the area, so simply divide the flux by the area to find the strength of the electric field there.