Using Gauss's Law on two separated, and infinite plates

[erick rocha]

Homework Statement

The figure shows cross-sections through two large, parallel, nonconducting sheets with identical distributions of positive charge with surface charge density σ = 1.06 × 10-22 C/m2. What is the y component of the electric field at points (a) above the sheets, (b) between them, and (c) below them?

Homework Equations

So since they have equal surface density, and their postive polarities are opposite of each other, I would think that they electric fields would just cancell each other out right? Appereantly not. Their elecctric field hace equal magnitude in opposite direction. Why would the doward compnent cancel the upward component?

The Attempt at a Solution

The E field in the in between the plates is zero since the inside component cancel each other out.
On the ouside...
E(net)= E(top)-E(bottom)
=σ/2ε-σ/2ε
=0
But the answer is actually
=σ/ε

 

[BvU]

Hello erick,

I wonder why you write E(net)= E(top)-E(bottom) instead of E(net)= E(top) + E(bottom). Are you aware the $\vec E$ field has a direction ? I think you are: after all, you let them cancel in the space between the plates. So what are the directions above both plates ? And below both plates ?

 

[erick rocha]

Hello erick,

I wonder why you write E(net)= E(top)-E(bottom) instead of E(net)= E(top) + E(bottom). Are you aware the $\vec E$ field has a direction ? I think you are: after all, you let them cancel in the space between the plates. So what are the directions above both plates ? And below both plates ?

Thanks for the welcome and the response BuV!
Conventionally we say that the E Field goes from positive to negative and since there is no field inside the object that must mean the E field vector from the top plate with a positively charge surface a must be pointing towards the positive y-axis towards infinity. Also the bottom plate of the bottom surface, that is also positively charged, must be pointing towards the negative y-axis towards infinity. The same logic as why the E field vectors in the middle canceled out.

 

[BvU]

Conventionally we say that the E Field goes from positive to negative and since there is no field inside the object that must mean the E field vector from the top plate with a positively charge surface a must be pointing towards the positive y-axis towards infinity

How about reasoning the other way around: E-field points away from positive charge, therefore the two (identical magnitude) contributions cancel in between and add up outside both plates !

 

[J Hann]

Review a Gaussian pillbox for a (single) non-conducting sheet and the derivation of the electric
field on either side of the sheet.
Now, as you have surmised, there can be no field between the two parallel sheets.
Now consider the fact that electric field lines originate on positive charges and end
on negative charges (they have to go somewhere).