# Solving Electric Fields in Surface Charge Density Problems

• latentcorpse
In summary, when dealing with a large horizontal sheet of surface charge density \sigma with a hole of radius b cut out, you can use the principle of superposition to subtract the electric field of the disc of radius b from the field of the sheet in order to find the total electric field directly above the centre of the hole. Additionally, by applying a Gaussian pillbox to an infinitely large charged sheet of surface charge density \sigma, you can obtain \vec{E(z)} = \frac{\sigma}{2 \epsilon_0} \vec{z} for the electric field. If the same charge is placed on the surface of a conductor, the field will double due to the arrangement of charges inside the conductor causing a net internal field
latentcorpse
ok if you could just tell em if this sounds alright.

(i) A large horizontal sheet of surface charge density $\sigma$ has a hole of radius b cout out of it. Find the electric field directly above the centre of the hole.

I already have expressions for the electric field due to the sheet and the disc of radius b on their own - can i just use the principle of superposition to subtract the field of the disc of radius b from the field of the sheet to get the total electric field?

(ii) By applying a Gaussian pillbox to an infinitely large charged sheet of surface charge density $\sigma$, I obtained $\vec{E(z)} = \frac{\sigma}{2 \epsilon_0} \vec{z}$ for the electric field. I am now asked why this field would double if the same charge were placed on the surface of a conductor.

I have a feeling this is because in the conductor the charges inside arrange themselves to give a net internal field of 0 and then this arrangement of the charges would cause a field to be generated outside the conductor equal to the initial external field, hence doubling it as a result of the superposition principle.

How do these ideas sound?

latentcorpse said:
... can i just use the principle of superposition to subtract the field of the disc of radius b from the field of the sheet to get the total electric field?
Of course you can.

## 1. What is the definition of electric field in surface charge density problems?

The electric field in surface charge density problems refers to the force per unit charge experienced by a charged particle at a specific point on the surface of a charged object. It is a vector quantity, meaning it has both magnitude and direction.

## 2. How is the electric field related to surface charge density?

The electric field is directly proportional to the surface charge density. This means that as the surface charge density increases, the electric field at a given point also increases. The electric field can be calculated by multiplying the surface charge density by a constant value, known as the permittivity of free space.

## 3. What are the units of electric field and surface charge density?

The SI unit for electric field is newtons per coulomb (N/C), while the SI unit for surface charge density is coulombs per square meter (C/m^2). However, other units such as volts per meter (V/m) and microcoulombs per square centimeter (μC/cm^2) can also be used.

## 4. How do you solve for the electric field in surface charge density problems?

To solve for the electric field in surface charge density problems, you can use the formula E = σ/ε, where E is the electric field, σ is the surface charge density, and ε is the permittivity of free space. You can also use the concept of superposition, where you calculate the electric field from individual charged particles and then add them together vectorially.

## 5. What are some real-world applications of solving electric fields in surface charge density problems?

Solving electric fields in surface charge density problems is important in various fields such as electrical engineering, physics, and chemistry. It is used in the design and analysis of electronic devices, such as capacitors and semiconductors. It is also relevant in understanding the behavior of charged particles in materials and in the study of atmospheric electricity, among others.

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