# Radial dependencies with electric field

1. Jan 23, 2016

### kiwibird4

so for uniform charge densities, a point "r" from the center of a ring of charge has an
E ∝ 1/r^2
a point "r" from center of a long line of charge has an
E ∝ 1/r
and for an infinite plane, a point "r" from it where r<<length of plane has
E not dependent on r

my question was why is it that a ring of charge has an inverse square proportionality compared to a line of charge? Does the point have a stronger dependency on distance because there is "more area" of a ring then simply a line's electric field?

Also, when I think about r becoming extremely large (so the point is very far away), wouldnt the ring of charge be more like a point charge but why would the line be seen less as a point charge since it is not an inverse squared dependency but an inverse linear dependency (if that even makes any sense)

2. Jan 23, 2016

### billslugg

For a ring of charge, when up close, the available charge would be producing an electric field in an ever growing series of nested cylinders. The area of the cylinders growing by the equation 2*r*pi.The drop off in field strength would thus be linear. As the ring receeds in the distance, it appears as a receeding point, thus the charge must be supporting a series of nested spheres, growing in surface area by 4*pi*r^2. The electric field thus dropping off by the inverse square rule. For the field near an infinite plane of charge, the charged plane supplies planes of the same size as the distance increases thus the field strength does not change.