Problem in orienting two plates as instructed in question

[gracy]

1.Homework Statement
Two large thin metal plates are parallel and close to each other. on their inner faces ,the plates have surface charge densities of opposites signs and magnitude 1.77 multiplied by 10^-11 coulomb per square meter.What is electric field
a)to the left of the plates
b)to the right of the plates
c)in between the plates

Homework Equations

[/B]E=σ/2ε0

The Attempt at a Solution

What is the proper orientation when the question says Two large thin metal plates are parallel and close to each other
I thought the following is correct

But this is not correct.
The answer is Fields due to both the plates will be equal and opposite so net field will be zero.I can not differentiate between the cases that are
to the left of the plate (2) and between the plates

 

[TSny]

In part (a), "to the left of the plates" refers to the far left region; that is, the region to the left of the left plate.
Likewise in part (b), "to the right of the plates" refers to the far right region; that is, the region to the right of the right plate.

 

[gracy]

In part (a), "to the left of the plates" refers to the far left region

Even if that's the case how come

The answer is Fields due to both the plates will be equal and opposite so net field will be zero.

 

[gracy]

I mean
Can electric field due to plate (2)go beyond the plate (1) i.e to the far left region
or even if it can ;would the electric field intensity of the charges of plate 2 be equal to that of plate one there in order to cancel the effect?

 

[ehild]

1.Homework Statement
Two large thin metal plates are parallel and close to each other. on their inner faces ,the plates have surface charge densities of opposites signs and magnitude 1.77 multiplied by 10^-11 coulomb per square meter.What is electric field
a)to the left of the plates
b)to the right of the plates
c)in between the plates

Homework Equations

[/B]E=σ/2ε0

The Attempt at a Solution

What is the proper orientation when the question says Two large thin metal plates are parallel and close to each other
I thought the following is correct
View attachment 88719

But this is not correct.
The answer is Fields due to both the plates will be equal and opposite so net field will be zero.I can not differentiate between the cases that are
to the left of the plate (2) and between the plates

Imagine one plate: When it is positively charged, the field lines emerge from it, and point away from the plate at both sides.
If the charge is negative, the field lines enter into the plate at both sides.
You can substitute the plates by planar distributions of charges. Both planes have their field everywhere, as shown in the picture. The orange lines are due to the positive charges, the blue lines belong to the negative ones. Apply he Superposition Principle: the resultant field is the sum of the fields of the individual planes.

 

[gracy]

would the electric field intensity of the charges of plate 2 be equal to that of plate one there in order to cancel the effect?

 

[ehild]

If the charges per unit surface area are equal, the fields are of equal magnitude.

 

[gracy]

If the charges per unit surface area are equal, the fields are of equal magnitude.

But electric field also depends on r i.e distance from source charge

 

[ehild]

But electric field also depends on r i.e distance from source charge

NO, if the plates are infinite (at least their lateral sizes are much larger than the distance between them). You wrote that E=σ/(2ε0) !

 

[gracy]

You wrote that E=σ/(2ε0) !

YES .I wrote that but I did not understand.

 

[gracy]

if the plates are infinite (at least their lateral sizes are much larger than the distance between them)

But it's beyond them not between them

 

[gracy]

NO, if the plates are infinite (at least their lateral sizes are much larger than the distance between them)

refers to the far left region

But it's beyond them not between them

 

[ehild]

YES .I wrote that but I did not understand.

It is symmetry again. The charge is evenly distributed on the plane. At a point the fields of the individual charges add as vectors. The parallel components cancel and only the perpendicular components remain. As the plane is of infinite extension, the field is the same above each points. If you integrate the contribution of all charges you will get the same result, independently how far the point is from the plate.

 

[ehild]

But it's beyond them not between them

The field of an infinite plate with even surface charge distribution is the same at both sides, only of opposite sign.

 

[gracy]

Ok.One more question If these are metal plates ,why charges are spread throughout the surface;charges should reside on borders/outer surface

 

[ehild]

Ok.One more question If these are metal plates ,why charges are spread throughout the surface;charges should reside on borders/outer surface

The plates were assumed of infinite sizes.
Even in case of real metal plates, not all charge reside along the borders. But it is true that they are spread on the surfaces.

 

[gracy]

As the plane is of infinite extension, the field is the same above each points.

Could you please elaborate this?

 

[gracy]

I am using this to understand
http://people.rit.edu/jdasps/jdainfo/313_tp/UniformlyChargedFinitePlane.pdf

 

[ehild]

I spoke about infinite plate.

 

[gracy]

Isn't there a little similarity between the two cases i.e finite plane when electric field is taken at mid point and infinite plate

 

[gracy]

As the plane is of infinite extension, the field is the same above each points

I am not able to comprehend this.

 

[gracy]

I am afraid ;It could be very silly question but I am serious about it.Will there be electric field intensity or force even when something comes in between(in the way of source charge to the point of interest) as in my question there is plate (1) in between the charges of plate 2(source charge) and the far left region but still electric field intensity is same as if nothing is in between.

 

[ehild]

The superposition principle says that you can calculate the resultant field of several objects separately, as if the other objects were not there, and then sum the individual fields. One plate has its own field, the other one has its own field, too. And the field of two plates is the sum of these contributions.

 

[gracy]

The superposition principle says that you can calculate the resultant field of several objects separately, as if the other objects were not there, and then sum the individual fields

Exactly What I wanted.Thanks @ehild

 

[ehild]

Exactly What I wanted.Thanks @ehild

Watch this video

 

[gracy]

Now only one thing is remaining
Why doesn't the electric field of an infinitely large plane depend on the distance from the plane?Please can you somehow make me understand.I will give my best.

 

[ehild]

The electric field lines are perpendicular to the infinite plane if the surface charge density is the same everywhere. That comes from symmetry. The plane is the same in every direction, so the field lines can not bend in any direction.
Assume a Gaussian surface as a cylinder, with axis perpendicular to the plane and enclosing an area A of the plane. The flux of field lines is due to the bases only, and it is Φ = 2EA = Aσ/ε₀, that is, E=σ/(ε₀) regardless of the distance from the plane.

 

[gracy]

it is Φ = 2EA = Aσ/ε0, that is, E=σ/(ε0) regardless of the distance from the plane

As far as derivation of this formula is concerned I understand .But I want to understand the concept,I want to understand how the effect of distance is nullified?I find this helpful.But still have something to ask.
https://www.quora.com/Why-doesnt-the-electric-field-of-an-infinitely-large-plane-depend-on-the-distance-from-the-plane
can I?

 

[ehild]

No field line crosses the side of the cylinder. It can be of any length, the flux across it is zero.

 

[gracy]

No field line crosses the side of the cylinder. It can be of any length, the flux across it is zero.

Sorry