Proving E&M homework problems

[mewmew]

So our latest E&M homework assignment out of griffiths has a bit of a twist. For all of the answers that we get we have to show that they seem reasonable. I know for instance with a charged solid sphere of radius R you could take R<<r where r is the distance away from the sphere and see that it looks like a point charge.

I am unsure however how to best show that the E fields of a charged spherical shell and an infinite line charge should be show to be reasonable though. Any hints on limits that may be appropriate to take in these cases or other methods that I should look at? Thanks for any help.

 

[OlderDan]

So our latest E&M homework assignment out of griffiths has a bit of a twist. For all of the answers that we get we have to show that they seem reasonable. I know for instance with a charged solid sphere of radius R you could take R<<r where r is the distance away from the sphere and see that it looks like a point charge.

I am unsure however how to best show that the E fields of a charged spherical shell and an infinite line charge should be show to be reasonable though. Any hints on limits that may be appropriate to take in these cases or other methods that I should look at? Thanks for any help.

At a point near the line charge and very far fom the sphere the result should reduce to the field from the line charge. At a point very far from the sphere on a line perpendicular to the line charge through the center of the sphere, the line charge field contribution should still dominate (1/r vs 1/r^2) and the contribution from the sphere should be point-like.

If the sphere is a neutral conductor whose charge redistributes in the presence of the line of charge, the field at any large distance from the sphere should reduce to the field from the line charge.