Why don't the electric field vectors cancel each other out in a non-conducting infinite plane sheet?  Why do these vectors not cancel each other out in spite of their being in the opposite directions?

• Hi Jay. Can you clarify exactly what you are asking? Do you mean an infinite charged sheet? If so, where do you think the vectors will cancel. At the mid plane of the sheet? If you would like to draw a diagram and upload it to an image hosting site we can insert the diagram into your question to help clarify it. – John Rennie Mar 3 at 10:23
• As shown in the image above the electric field vectors are going in opposite directions above and below the plane. – Jay Sen Mar 3 at 10:32
• The upwards field exists only above the sheet and the downwards field exists only below the sheet. The only place where both the two fields exist is right in the centre of the sheet, and in that plane they do cancel. Everywhere else they can't cancel because they don't overlap. – John Rennie Mar 3 at 10:38
• Consider it being point charges smeared across the plate. The field lines are supposedly propagating off the same set of charged particles in all directions, and the approximate resultant vector direction is the upward and downward. Try drawing a set of positive point charges horizontally and then resolve the approximate directions of their net combined field effect. – TechDroid Mar 3 at 10:44
• If you want to quote a part of your text, please type it out rather than posting a picture. The relevant information won't show up if other people search for a similar question if it is in a picture. – Aaron Stevens Mar 3 at 11:01

In order to superimpose two or more electric fields, they must be defined in the same region. In other words $$\mathbf E=\mathbf E_1(x_0,y_0)+\mathbf E_2(x_0,y_0)$$ for some point in space $$(x_0,y_0)$$

In your case, $$\mathbf E_1$$ and $$\mathbf E_2$$ exist in different regions of space. Therefore, you can't superimpose them and they don't cancel. It's kind of like asking if I put my car in drive and your put yours in reverse why both of our cars don't just stay still.

Perhaps your confusion lies in thinking that the field vectors in your picture only exist on the sheet. This is not the case. At every point $$(x,y,z)$$ in space there is an electric field. For $$z>0$$ the field points upward, for $$z<0$$ the field points downward. You can't add the upward and downward fields together because they exist in different regions of space.

• Then how and why are we adding them up? – Jay Sen Mar 3 at 11:01
• @JaySen We aren't adding them up. That's what I'm trying to say. The two fields that you say should cancel out exist in different regions of space, so they don't add up and don't cancel – Aaron Stevens Mar 3 at 11:02
• I think we add them up for getting the total electric field. – Jay Sen Mar 3 at 11:04
• When doing field line vector resolution, we aren't adding the field or field lines itself, but the effect vector direction of the field(s). – TechDroid Mar 3 at 11:06
• Sorry but i haven't understood this yet. – Jay Sen Mar 3 at 11:14

This is a inside look at the atomic scale: The field effect is radial and the intersecting field effects sort of cancles out. The direction lines are not forces on the plate but the field effect direction from the plate. You only do that sort of vector cancellation if the force vectors are rather on the plate. If another lone floating positively charged particle falls anywhere in this region, those field lines are the direction of force on the charge. We aren't vectorially resolving the field lines, but rather the force effect on another charged body.