A line of charge with charge density = 2.0 C/m issurrounded by a cylindrical she

Question

A line of charge with charge density = 2.0 C/m issurrounded by a cylindrical shell of radius R = 25.0 cm along itscentral axis. What is the surface charge density on the inside of thecylinder? What is the surface charge density on the outside of thecylinder? I'm not sure now to convert from line to surface chargedensity . Do we use EA=Qenc/0 and if so,how? If someone could explain each step, I would greatlyappreciate it!! A line of charge with charge density = 2.0 C/m issurrounded by a cylindrical shell of radius R = 25.0 cm along itscentral axis. What is the surface charge density on the inside of thecylinder? What is the surface charge density on the outside of thecylinder? I'm not sure now to convert from line to surface chargedensity . Do we use EA=Qenc/0 and if so,how? If someone could explain each step, I would greatlyappreciate it!!

Explanation / Answer

The induced charge on length L of the cylinder must equal thecharge on length L of the enclosed wire. The problem does not state but implies that the cylinder is aconductor. Since there is no electric field within the conductor thetotal charge enclosed by an imaginary surface, a cylinder, within the conductor must enclose no net charge. 2 R L = L     for thesecharges to be equal Thus = / (2 R) (Also, we know the field at the surface of a conductor is E = / 0    then E = / (2 R 0)  which is the field due to a line charge at distance R) Also, the charge on the outside of the cylinder must beequal and opposite the induced charge on the inside of the cylinder since the netcharge on the cylinder is zero. then E = / (2 R 0)  which is the field due to a line charge at distance R) Also, the charge on the outside of the cylinder must beequal and opposite the induced charge on the inside of the cylinder since the netcharge on the cylinder is zero.

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