# Infinite Sheets of Charge

• heartofaragorn
In summary, the conversation discusses an infinite sheet of charge with a surface density of -3 micro C/m^2 and a thick, infinite conducting slab with a net charge per unit area of 5 microC/m^2. The task is to calculate the surface charge densities on the left and right hand faces of the slab, with a note on their relationship. The attempt at a solution involves using the formula E = density / permittivity of free space (epsilon o) to determine the distribution of negative and positive charges on the surfaces. However, the correct answer cannot be obtained using this approach.
heartofaragorn

## Homework Statement

An infinite sheet of charge, oriented perpendicular to the x-axis, passes through x = 0. It has area density = -3 micro C/m^2. A thick, infinite conducting slab, also oriented perpendicular to the x-axis, occupies the region between x=a and x=b where a = 4 cm and b=5 cm. The conducting slab has a net charge per unit area = 5 microC/m^2. Calulate the surface charge densities on the left hand and right had faces of the conducting slab. You may also find it useful to note the relationship between them.

## Homework Equations

E = density / permittivity of free space (epsilon o)
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## The Attempt at a Solution

According to my physics book, since the inside of the conductor has an electric field of zero, one can assume that the charge on the surfaces are negative and positive. I reasoned that the negative charge would like closer to the y-axis whereas the positive charge would lie on the other side. I tried using the formula above, but I'm guessing it is the wrong formula since I cannot get the correct answer this way. I also tried answers such as -3 micro C and +8 micro C to balance out the total charge of 5 micro C. Where am I going wrong?

It would help if I attached the picture!

#### Attachments

• Sheets.gif
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I would first like to commend you for attempting to solve this problem and for recognizing that your initial approach may not be yielding the correct answer. It shows that you are thinking critically and seeking a deeper understanding of the material.

In this scenario, the conducting slab is acting as a capacitor, with the infinite sheet of charge serving as one plate and the conducting slab serving as the other. The surface charge densities on the left and right faces of the slab will depend on the electric field created by the infinite sheet of charge and the distance between the two plates.

To calculate the surface charge densities, we can use the equation for electric field between two parallel plates:

E = (density * d) / (2 * permittivity of free space)

Where d is the distance between the plates. In this case, d = b-a = 1 cm.

We can then use the fact that the electric field is the same at all points between the plates to set up the following equation:

E = (-3 micro C/m^2) / (2 * permittivity of free space) = (5 microC/m^2) / (2 * permittivity of free space)

Solving for the permittivity of free space, we get:

permittivity of free space = (-3 micro C/m^2) / (5 microC/m^2) * 2 = -0.6

This is not possible, as the permittivity of free space is a constant value of approximately 8.85 x 10^-12 F/m. This means that our initial assumption of the electric field being the same at all points between the plates is incorrect.

In order to solve this problem, we need to consider the fact that the electric field created by the infinite sheet of charge will not be uniform between the plates. It will be stronger closer to the sheet and weaker further away. This means that we cannot use the same equation for electric field as before.

Instead, we can use Gauss's law to determine the electric field at a point between the plates. Gauss's law states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space. In this case, we can use a Gaussian surface between the plates to determine the electric field.

Using this approach, we can set up the following equation:

E * 2 * d = (-3 micro C/m^2) / permittivity

## 1. What is an infinite sheet of charge?

An infinite sheet of charge is a theoretical concept in electrostatics where a two-dimensional surface is uniformly charged with an infinite amount of charge. It is a simplification used to model certain electrical systems and can be thought of as a flat, infinitely large plane with a constant surface charge density.

## 2. Can infinite sheets of charge exist in real life?

No, infinite sheets of charge do not exist in the physical world as they are purely theoretical. However, they can be used to approximate the behavior of certain electrical systems and provide valuable insights into electrostatics.

## 3. How does the electric field vary around an infinite sheet of charge?

The electric field around an infinite sheet of charge is constant and perpendicular to the surface of the sheet. This means that the electric field lines are parallel and evenly spaced, creating a uniform electric field.

## 4. How does the electric potential vary around an infinite sheet of charge?

The electric potential around an infinite sheet of charge also remains constant and perpendicular to the surface of the sheet. This means that the electric potential decreases as you move further away from the sheet, creating a linear potential gradient.

## 5. How do infinite sheets of charge affect other charged particles?

Infinite sheets of charge exert a force on other charged particles, causing them to experience an electric field and potentially move. The direction and strength of the force depend on the charge and position of the particle relative to the sheet. This interaction is crucial in understanding the behavior of electrical systems.

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