# Finding the E due to a non-uniform surface charge distribution in 3D

1. Sep 17, 2014

### Shostakovich

1. The problem statement, all variables and given/known data

Here is the question, which itself is rather confusing.

A nonuniform surface charge lies in the yz plane. At the origin, the surface charge den- sity is 3.5 μC/m^2. Other charged objects are present as well. Just to the right of the origin, the electric field has only an x component of magnitude 4.8 × 10^5 N/C.
What is the x component of the electric field just to the left of the origin? The permittivity of free space is 8.8542 × 10^−12 C2/N · m^2.

2. Relevant equations

ø=∫E.dA = Q(enclosed)/ε(naught)

σ = Q/A

3. The attempt at a solution

So i drew the pictures, a 2D surface lying in the yz, with a point x with electric field value 4.8e5 N/C just to the right on the positive axis.
I thought to myself the field will just be negative because its on the opposite side? Nope.
Maybe it's the same? Nope.
I then tried finding the difference, to no avail, and now I'm just stuck.

Is there a better way for me to think about this problem that I'm not seeing, or is it just that obscure?

2. Sep 17, 2014

### Staff: Mentor

Hmm. Suppose that "just to the right of the origin" implies that the observer there is so close that he "sees" the surface charge in the yz plane as an infinite sheet of charge with the given charge density. What field strength would he expect to see from it? How does that compare to what he actually observes? If there's a difference, what then?

3. Sep 17, 2014

### Shostakovich

As you probably well know, the Electric field due to an infinite sheet is σ/(2ε(naught)). But this gives something about 2.43 times smaller than what was given. Does this proportion have anything to do with how the field distributes itself?

Last edited: Sep 17, 2014
4. Sep 17, 2014

### Staff: Mentor

The proportion is not particularly relevant. What is relevant is that the observed field strength is not entirely accounted for by the sheet's field.

If the field due to the sheet of charge doesn't account for the net field observed, what does that tell you about the contribution from the "other charged objects" that were mentioned? What happens if your observer moves (a very small distance indeed) from the right to the left of the sheet?