# Electric field outside a infinitely long capacitor

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.

• 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. Aug 13, 2016 at 18:53
• @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? Aug 14, 2016 at 4:20
• 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. Aug 14, 2016 at 4:25