Infinite sheets of charge w/ conducting slab

In summary, the problem involves two infinite sheets with different surface charge densities perpendicular to the x-axis and an infinite conducting slab with a net charge per unit area placed between them. The goal is to calculate the x-component of the net electric field at x = 0 and the surface charge density on each side of the slab. The equation E=\sigma/2\epsilon0 can be used to calculate the electric field, but the different surface charge densities on each side of the slab make it more complicated. Both sides of the slab must have a surface charge density that adds up to the total surface charge density of the slab.
  • #1
rgalvan2
30
0

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[tex]\mu[/tex]C/m^2
σ2=1.5[tex]\mu[/tex]C/m^2
σC=-3[tex]\mu[/tex]C/m^2
a=2cm

Homework Equations


E=[tex]\sigma[/tex]/2[tex]\epsilon[/tex]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!
 
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  • #2
What are you asked to find?
 
  • #3
Oops sorry:
Calculate the x-component of the net electric field at x = 0.
I figured that part out though.
The next part asks to calculate the surface charge density on each side of the slab. I'm not sure how to do that. I do know that both sides need to equal the total surface charge density of the slab. Is that right?
 

1. What is an infinite sheet of charge?

An infinite sheet of charge is a theoretical concept in physics where an infinitely large, thin sheet is uniformly charged with a specific electric charge per unit area. This means that the charge is spread out over the entire surface of the sheet and has no thickness.

2. How does an infinite sheet of charge affect the electric field?

An infinite sheet of charge creates a uniform electric field that is perpendicular to its surface. This means that the electric field lines are parallel and evenly spaced, pointing away from the positively charged sheet and towards the negatively charged sheet.

3. What is a conducting slab in relation to an infinite sheet of charge?

A conducting slab is a material that allows electric charges to move freely. In the case of an infinite sheet of charge, a conducting slab can be placed above or below the sheet to create a capacitor. The electric field between the sheet and the slab will be affected by the charges on the sheet and the properties of the slab.

4. How does the distance from the infinite sheet of charge affect the electric field?

The electric field strength decreases as the distance from the infinite sheet of charge increases. This is because the electric field lines spread out as they move away from the sheet, resulting in a weaker field. The relationship between distance and electric field strength follows an inverse square law.

5. Can an infinite sheet of charge and a conducting slab have a net charge of zero?

Yes, it is possible for an infinite sheet of charge and a conducting slab to have a net charge of zero. This can be achieved by placing equal and opposite charges on the sheet and the slab. In this case, the electric field between them would cancel out, resulting in a net electric field of zero.

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