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enter image description here If we construct the gaussian surface as shown (cylinder with one of the discs in the negatively charged plate of the capacitor) and the field at P is to be calculated, then as the total charge within the surface is zero so total flux will be zero. And the electric field is at all points normal to the plane of the plates of the infinitely long capacitor and also the discs of the cylinder, so the electric field at P must be zero, but P is closer to the positively charged plate and thus an outward electric field must be present at P. I am unable to resolve this contradiction, any help will be appreciated.

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  • $\begingroup$ You can't construct a Gaussian surface around an infinite object. Mathematically Gauss is limited to finite volumes and surfaces. In general you need to stop thinking about infinite objects. They don't exist. What you need to do is to learn to properly approximate the fringe fields of finite objects. $\endgroup$
    – CuriousOne
    Aug 13 '16 at 18:53
  • $\begingroup$ @CuriousOne i don't think, there should be a problem constructing a finite gaussian surface around an infinite object. Doesn't the infinite length of the plate only serve to give the direction of the electric field perpendicular to it? $\endgroup$
    – user329387
    Aug 14 '16 at 4:20
  • $\begingroup$ You can, of course, construct a finite surface, which now will intersect a charge... and all you have to do is to integrate over that infinity. Or... you avoid all of that and you accept that infinite objects don't exist and that the only reason why some textbook authors are summing them with magical hands is to spare themselves having to explain to you how to properly handle edge effects. $\endgroup$
    – CuriousOne
    Aug 14 '16 at 4:25
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An infinite big plate creates an uniform electric field perpendicular to it. This means that no matter how close or how far you are from that plate, you measure the same electric field.

Thus, when you put two opposite charged plates to form a capacitor, the fields between the plates will be directed the same way and this means that you have a non zero electric field in the inside, while the fields outside the plates will cancel out and you have a null electric field outside.

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