How Do You Find the Field Inside a Polarized Cylinder?

In summary, The problem at hand is to solve for the electric field inside a long cylinder with a uniform polarization perpendicular to the axis. The equations provided, \rho_b=P\cdot\hat{n} and \sigma_b=-\nabla\cdot P, may not be necessary for this problem. It may be more helpful to look at Gauss's Law inside and outside the cylinder and keep in mind that \rho_b and \sigma_b represent the bound charges, not the electric field. It is unclear if the use of these equations was suggested by the professor or assumed by the student.
  • #1
shaun_chou
13
0

Homework Statement


This problem is at Griffiths 4.13. A very long cylinder of radius a with a uniform polarization perpendicular to the axis. The question is to solve for the field inside the cylinder.


Homework Equations


[tex]\rho_b=P\cdot\hat{n}[/tex] and [tex]\sigma_b=-\nabla\cdot P[/tex]


The Attempt at a Solution


I can't find a good solution using above equations. Can anyone help me? Thanks a lot!
 
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  • #2
I don't think you need those two equations for this problem. You should be looking at Gauss's Law inside and outside the cylinder.
 
  • #3
Also, [itex]\rho_b[/itex] and [itex]\sigma_b[/itex] are the bound charges (volume and surface respectively) and are not the electric field.

Is your professor suggesting you solve the problem using them, or did you assume you should since the question by Griffiths is right after the section on the bound charges?
 

FAQ: How Do You Find the Field Inside a Polarized Cylinder?

1. What is a polarized cylindrical field?

A polarized cylindrical field refers to the electric field that is created by a charged cylinder that has a polarized surface. The electric field lines of such a field are perpendicular to the surface of the cylinder and vary in strength depending on the distance from the cylinder.

2. How is the electric field strength in a polarized cylindrical field calculated?

The electric field strength in a polarized cylindrical field can be calculated using the formula E = (ρ / 2ε0) * (1 + cosθ), where ρ is the surface charge density, ε0 is the permittivity of free space, and θ is the angle between the electric field line and the surface of the cylinder.

3. What is the direction of the electric field in a polarized cylindrical field?

The electric field lines in a polarized cylindrical field are perpendicular to the surface of the cylinder, pointing away from the positively charged end and towards the negatively charged end.

4. How does the electric field in a polarized cylindrical field change with distance?

The strength of the electric field in a polarized cylindrical field decreases as the distance from the cylinder increases. This decrease follows an inverse square law, meaning that the electric field strength is inversely proportional to the square of the distance from the cylinder.

5. What are some real-world examples of polarized cylindrical fields?

Polarized cylindrical fields can be found in many everyday objects, such as capacitors, batteries, and electronic devices. They are also present in natural phenomena, such as lightning strikes and the Earth's magnetic field.

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