# Electric field near infinite charged sheet and point charge

1. Oct 5, 2012

### prakharj

Electric field near charged sheet is sigma/2E
Which is independent of the distance from it.. However In case of point charge, as we go very close to it, magnitude of electric field tends to infinity.. But why doesn't this happen with charged sheet, i mean it can also be considered as combination of point charge, so while going very close to it, mag. Of electric field must increase, instead of remaining constant..
(please clear me up, i'm new in this area)
thank you.

2. Oct 5, 2012

### tiny-tim

hi prakharj!
two alternative explanations …

i] the field lines are parallel for a plane charge (so the strength stays the same), but they converge for an isolated charge (so the strength gets larger and larger)

ii] the field does tend to infinity if you approach a charged sheet, but only if you are heading directly towards one of the charges …

most of a charged sheet is empty space, so on average the field stays finite

3. Oct 5, 2012

### rcgldr

In an ideal charged sheet, the charge is uniformly spread so that amount of charge per unit area is constant, so no matter how close you get to the sheet the field remains constant (until you actually reach the surface of the sheet).

The forces (upon a point charge) parallel to the surface of the sheet cancel, so only the component of force perpendicular to the sheet from each point on the sheet affects the field at some point at some distance from the sheet. Say you only consider the portion of the force that is limited to some maximum angle from perpendicular. The shape of this component is a cone with it's circular base at the sheet and it's peak at the point. If you double the distance from the sheet, the inverse square law states the force per unit area is 1/4th of what it was before, but that area of the base of that cone has quadrupled, so that component of force within a cone with some fixed sub-tended angle remains constant regardless of distance from the sheet. Then you can let that subtended angle of the cone increase towards a limit of π, and the effect remains the same.

This cone analogy is one of the ways calculus can be used to calculate the force (the cone analogy is similar to the field from a disk where the ratio of height versus radius is fixed). The force from a thin ring of charge with a fixed charge per unit length of the ring can be calculated, and then the force from an disk composed of an infinite number of thin rings can be calculated, as is done here:

http://hyperphysics.phy-astr.gsu.edu/%E2%80%8Chbase/electric/elelin.html#c3 [Broken]

As R → ∞, the field → k σ 2 π.

The alternative in calculus is to consider the force from an infinitely long thin line with fixed charge per unit length, then calculate the force from an infinite plane made up of an infinite number of those lines.

Last edited by a moderator: May 6, 2017