# Surface Charge Density of Coaxial Cylinder with Canceling Electric Fields

• engnrshyckh
In summary, the conversation discusses the calculation of the surface charge density of a thin-walled non-conducting coaxial cylinder that encloses a long straight wire with a fixed negative charge density. The electric field of the wire is determined using the equation E=lamda/2pi€r and the total electric field is required to be zero, which leads to the conclusion that the cylinder must have the opposite charge density as the wire. To convert the linear charge density to a surface charge density, the shell must have the same charge per unit length as the wire.
engnrshyckh
a long straight wire has fixed -ve charge density of 39nC/m. the wire is enclosed by thin wall non conducting coaxial cylinder of radius 1.7m. the shall has positive charge density and its Field is such as that it will cancel the field due to wire. what will be the surface charge density of cylinder.

E=lamda/2pi€r
gausses law

## The Attempt at a Solution

first i have found the the electric field of wire enclosed in cylinderusing equation E=lamda/2pi€r. then as given total electric field must be zero so E for cylinder must be same in magnitude as of wire but opposite sign. but i have no idea i am attempt towards solution is right or wrong any help??

From what I manage to understand, yes your attempt is correct. it should give you the charge on the cylinder. What went wrong then?

Since electric field lines start and end on charges, the shell must have the same charge per unit length
as the wire. So it appears that you need to convert a linear charge density to a surface charge density.

thhanks

## What is Gauss' law and how is it used?

Gauss' law is a fundamental law in electromagnetism that relates electric charges to the electric field they create. It states that the total electric flux through a closed surface is equal to the total enclosed charge divided by the permittivity of free space. It is used to calculate the electric field at a point due to a distribution of charges and is an important tool in solving a variety of electrostatics problems.

## What is electric flux and how is it related to Gauss' law?

Electric flux is a measure of the flow of electric field through a given surface. It is defined as the dot product of the electric field and the surface area. Gauss' law relates the electric flux through a closed surface to the enclosed charge, showing that the electric field is directly proportional to the charge enclosed by the surface.

## How is Gauss' law used to find the electric field of a point charge?

To find the electric field of a point charge using Gauss' law, a Gaussian surface is chosen such that the charge is enclosed within it. The electric flux through this surface is then calculated and equated to the enclosed charge divided by the permittivity of free space. This allows for the electric field to be calculated at any point outside the charge, using the inverse square law.

## What are some key applications of Gauss' law in real-world situations?

Gauss' law has numerous applications in practical situations, such as in the design of electronic devices, capacitors, and antennas. It is also used in the study of lightning strikes and the behavior of electric fields in lightning rods. Additionally, it is used in medical imaging techniques such as electrocardiograms and electroencephalograms.

## What are the limitations of Gauss' law?

Gauss' law is only applicable to electrostatic situations, where charges are not moving. It is also limited to situations where the electric field is constant over the chosen Gaussian surface. In cases where the field is not constant or when charges are moving, other laws such as Ampere's law or Faraday's law must be used.

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