Electrostatic problem

dingo_d

1. The problem statement, all variables and given/known data

I'm looking at Y.K.Lim's Problems and solutions in Electromagnetism and there's one thing that's confusing me:



2. Relevant equations

Where does the square in r comes from? When in the beginning it says that the electric field is:

[tex]E=A\frac{e^{-br}}{r}e_r[/tex] not[tex]E=A\frac{e^{-br}}{r^2}e_r[/tex]

What am I missing?

And what should [tex]e_r[/tex] stand for? Charge?

hikaru1221

This E-field is not due to a single charge. It is due to a distribution of charges, so it needs not be proportional to r^2. For example, a uniformly charged plane produces uniform E-field on each side of the plane, obviously not proportional to distance^2, correct?
[tex]e_r[/tex] is the unit radius vector.

dingo_d

Ok it needs not be proportional to r^2, but why did he put it then? When taking the divergence of the field?

hikaru1221

Oh I see. Then it seems to me that it's a typo

dingo_d

Oh, I thought it's something new I didn't know XD