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.
Yes it is right to say that electric field by a finite plate is not constant and zero at infinity. But in case of capacitors,the separation between the plates is so small as compared to dimensions of plate that with respect to the separation between the plates the plate itself can be considered as infinite. It is just a relative assumption to simplify things. Take care :-)