Why is this electric field due to one plate of a capacitor $\sigma / 2 \epsilon_0$ when the capacitor plates are finite?

We know that electric field due to an INFINTE large sheet is constant and at INFINTY the electric field is not zero. But say if I take a finite sheet of length l and width w. Then the electric field would be zero at infinity. Also we say that electric field is constant for a infinite sheet but for a finite sheet of length l and width w , it won't be constant. Electric field for a finite long sheet at a point x above it whose length is l and width is w is given in th following website: http://people.rit.edu/jdasps/jdainfo/313_tp/UniformlyChargedFinitePlane.pdf Just give a look where E finite plane is written in tha website....in the second page ....And that formula is in box. When you put x as infinity you would make arctan tending towards zero and hence the you would make the electric field when x is tending to infinity as zero. So the formula E=sigma/2ϵ0 (which is constant) is only for the plane sheet which is infinitely large and for this infinitely large sheet of charge at infinty the field is same i.e. E=Sigma/2ϵ0. But for a finite sheet at infinty the electric field is zero and also for a finite sheet the electric field is not constant with changing the distance from the plate. Then in the case of capacitors, whose plates are finite, why then we say that electric field due to one of its plate is sigma/2ϵ0? So my first question: it right to say that for any plane sheet of charge which is not infintely large electric field is not constant and at inifinty the electric field is zero? And my second question: plz explain why we say that electric field due to one of the capacitor plate is sigma/2ϵ0 while the capacitor plates are finite.

• There are no infinitely large objects in physics and "infinity" is only physics speech for "far enough". The better way to work these kinds of problems would be to say "sufficiently close to a finite charged plate", but many textbooks are setting their students up for failure on real world problems by making unphysical simplifications like above. One can only hope that future textbook authors will do better. So what is "sufficiently close"? It's in the part of the field above where the charge density on the plate is almost constant and the field lines are almost parallel. – CuriousOne Jun 14 '15 at 7:32
• Two truly-infinite parallel plates cannot be at different potentials since they "meet" at infinite. – Rol Jun 14 '15 at 8:18