# Electric Field Between Two Infinite Sheets of Charge

• BRuss9807
In summary, the problem involves calculating the potential difference between two points, P and S, located at specific positions in relation to two infinite sheets of charge and an uncharged conducting slab. The attempt at a solution involved using the electric field at point P, which was assumed to be constant, to calculate the potential difference. However, the feedback pointed out the need to account for the electric field not being constant between the two points, as the conducting slab would create a region with no electric field. By considering this, the correct potential difference of 0 V was obtained.
BRuss9807

## Homework Statement

An infinite sheet of charge is located in the y-z plane at x = 0 and has uniform charge denisity σ1 = 0.57 μC/m2. Another infinite sheet of charge with uniform charge density σ2 = -0.39 μC/m2 is located at x = c = 28.0 cm.. An uncharged infinite conducting slab is placed halfway in between these sheets ( i.e., between x = 12.0 cm and x = 16.0 cm). What is V(S) - V(P), the potentital difference between point P, located at (x,y) = (6.0 cm, 0.0 cm) and S, located at (x,y) = (22.0 cm, -16.0 cm)?

https://www.smartphysics.com/Content/Media/Images/EM/06/h6_planeA.png

## The Attempt at a Solution

I have attempted at an answer and obtained the result of 8685.87 V.

This answer came by way of:

Electric field at point P:
E = (σ1/2ε)-(σ2/2ε) = 54286.72 (N/C) or (V/m)
Set this point to be the zero potential energy position, and since the electrical field is constant, or so I thought, in the x direction, with no component in the y direction, I simply took the difference in x positions of the two points. 22cm-6cm= 16cm, therefore the ΔV between these two points is (54286.72V/m)*(.016m)= 8685.87 V

The feedback to this answer says that I need to account for the Electric field not being constant between these two points. What I am confused about is that I thought the electric field between these two points would be constant. Since a single infinite plate will have a constant electric field that is not dependent on distance from the plate I assumed that the electric field between two of these plates would also be constant. Thank you to anyone that can explain this to me, I can't seem to figure it out and its driving me crazy.

Last edited by a moderator:
BRuss9807 said:

## Homework Statement

An infinite sheet of charge is located in the y-z plane at x = 0 and has uniform charge denisity σ1 = 0.57 μC/m2. Another infinite sheet of charge with uniform charge density σ2 = -0.39 μC/m2 is located at x = c = 28.0 cm.. An uncharged infinite conducting slab is placed halfway in between these sheets ( i.e., between x = 12.0 cm and x = 16.0 cm). What is V(S) - V(P), the potentital difference between point P, located at (x,y) = (6.0 cm, 0.0 cm) and S, located at (x,y) = (22.0 cm, -16.0 cm)?

https://www.smartphysics.com/Content/Media/Images/EM/06/h6_planeA.png

## The Attempt at a Solution

I have attempted at an answer and obtained the result of 8685.87 V.

This answer came by way of:

Electric field at point P:
E = (σ1/2ε)-(σ2/2ε) = 54286.72 (N/C) or (V/m)
Set this point to be the zero potential energy position, and since the electrical field is constant, or so I thought, in the x direction, with no component in the y direction, I simply took the difference in x positions of the two points. 22cm-6cm= 16cm, therefore the ΔV between these two points is (54286.72V/m)*(.016m)= 8685.87 V

The feedback to this answer says that I need to account for the Electric field not being constant between these two points. What I am confused about is that I thought the electric field between these two points would be constant. Since a single infinite plate will have a constant electric field that is not dependent on distance from the plate I assumed that the electric field between two of these plates would also be constant. Thank you to anyone that can explain this to me, I can't seem to figure it out and its driving me crazy.
What is the electric field between x = 12.0 cm and x = 16.0 cm , i.e., inside the conducting slab ?

Last edited by a moderator:
Wow thank you so much SammyS. I cannot believe I forgot that the area inside the conductor would not contain an electric field, therefore no contribute to the potential change. True testament to the need to simply think the problem through completely. Thanks again.

## 1. How do you calculate the electric field between two infinite sheets of charge?

The electric field between two infinite sheets of charge can be calculated using the formula E = σ/2ε0, where σ is the surface charge density and ε0 is the permittivity of free space.

## 2. What is the direction of the electric field between two infinite sheets of charge?

The electric field between two infinite sheets of charge is always perpendicular to the sheets and points away from the positively charged sheet and towards the negatively charged sheet.

## 3. How does the distance between the two sheets affect the electric field?

The distance between the two sheets has no effect on the electric field between them. The electric field is solely determined by the surface charge density of the sheets.

## 4. Is the electric field between two infinite sheets of charge uniform?

Yes, the electric field between two infinite sheets of charge is uniform, meaning it has the same magnitude and direction at all points between the sheets.

## 5. Can the electric field between two infinite sheets of charge be negative?

Yes, the electric field between two infinite sheets of charge can be negative. This occurs when the surface charge density of the sheets is opposite in sign, resulting in an attractive force between the sheets.

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