How Does a Conducting Slab Affect Electric Fields Between Charged Sheets?

• rgalvan2
In summary, the electric field in the space between the two infinite sheets with surface charge density σ1 and σ2, respectively, is 1.5 V/m.
rgalvan2

Homework Statement

Two infinite sheets with surface charge density σ1 and σ2, respectively, are oriented perpendicular to the x-axis. An infinite, conducting slab of thickness a is placed between the charged sheets as shown in the figure. The conducting plate has a net charge per unit area of σC.

σ1=8.85$$\mu$$C/m^2
σ2=1.5$$\mu$$C/m^2
σC=-3$$\mu$$C/m^2
a=2cm

Homework Equations

E=$$\sigma$$/2$$\epsilon$$0

The Attempt at a Solution

I figured since the magnitude of the electric field is not determined by displacement, I could just use the above equation. The only problem it that the conducting slab has different surface charge density on each side and I'm not sure how to start this. I have an exam tomorrow so any help is greatly appreciated!

I also attached a picture of the problem.

The Attempt at a Solution

Attachments

• conducting slab.gif
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The electric field for the two charged sheets can be calculated using the equation E=σ/2ε₀.For the first sheet (σ1): E1 = 8.85μC/m²/2ε₀ = 4.425 V/mFor the second sheet (σ2): E2 = 1.5μC/m²/2ε₀ = 0.75 V/mThe electric field for the conducting slab can be calculated by subtracting the electric fields of the two charged sheets:Eslab = E1 - E2 = 3.675 V/mThe net charge per unit area of the conducting slab is σC=-3μC/m², so the electric field inside the slab is equal to -3μC/m²/2ε₀ = -1.5V/m. The electric field at the boundaries of the slab can be calculated by adding the electric fields of the two charged sheets: Eb = E1 + E2 = 5.175 V/mThe total electric field in the space between the two sheets is thus equal to Eb - Eslab = 5.175 - 3.675 = 1.5 V/m.

1. What is an infinite sheet of charge?

An infinite sheet of charge is a theoretical model used in electrostatics to represent a large, flat surface with a uniform distribution of charge. It is assumed to have an infinite length and width, but a finite thickness.

2. How does an infinite sheet of charge behave?

An infinite sheet of charge behaves as if all of its charge is concentrated on the surface, and there is no electric field inside the sheet. This means that the electric field above and below the sheet is constant and perpendicular to the surface.

3. How is the electric field calculated for an infinite sheet of charge?

The electric field for an infinite sheet of charge can be calculated using Gauss's Law. The electric field is equal to the surface charge density divided by the permittivity of free space (E = σ/ε0), where σ is the charge per unit area on the sheet.

4. Can an infinite sheet of charge exist in reality?

No, an infinite sheet of charge is a theoretical model used for simplification in calculations. In reality, all objects have a finite size and cannot have an infinite charge distribution.

5. How is the electric potential calculated for a point above or below an infinite sheet of charge?

The electric potential for a point above or below an infinite sheet of charge can be calculated using the equation V = -Ed, where E is the electric field and d is the distance from the point to the sheet. This assumes that the electric potential is zero at infinity.

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