An infinitely long insulating cylinder of radius R has a volume charge density t
ID: 1589094 • Letter: A
Question
An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as (picture) , where ?o, a and b are positive constants and r is the distance from the axis of the cylinder. Use Gauss’s law to determine the magnitude of the electric field at radial distances (a) r < R and (b) r > R
I've done up to (a) , I don't know how to do (b). please, help me
6. An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as p- po (awhere po a and b are positive constants and r is the distance from the radius asp= Ao (a-: radius as = (a--) , where po, a and b are positive constants and r is the distance from the axis of the cylinder. Use Gauss's law to determine the magnitude of the electric field at radial distances (a) r RExplanation / Answer
When r>R, Gauss’s law becomes,
E(2pi*r) = (0/ 0)*integration [(a- (r/b))*2pi*rdr] (limits 0 to R)
or outside the cylinder, E = (0R2/20r) [a 2R/3b]
When r is large compared to the cylinder radius R, the field must decrease like that of a uniform line of charge. That is, it must decrease faster than the field due to a uniform infinite sheet (which is constant), but not as fast as the field due to a point charge (which decreases with 1/r2 ).
E 1/r