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Thin conducting plate boundary conditions

by nutan123
Tags: boundary, conditions, conducting, plate
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nutan123
#1
Sep14-09, 12:59 PM
P: 2
1. The problem statement, all variables and given/known data

A thin conductor plate is in free space. Its conductivity is finite and thickness is approaching zero. Relate the tangential electric field in either side of the conductor. Repeat for tangential magnetic field. How are electric and magnetic fields related.

2. Relevant equations
Standard boundary conditions
[tex]\textbf{n}[/tex]*([tex]\textbf{h2}[/tex]-[tex]\textbf{h1}[/tex])=[tex]\rho[/tex]
[tex]\textbf{n}[/tex]*([tex]\textbf{e2}[/tex]-[tex]\textbf{e1}[/tex])=0


3. The attempt at a solution
Tried to apply the boundary conditions on each of the boundries. However, could not relate the field from both the sides.
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
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gabbagabbahey
#2
Sep16-09, 04:02 PM
HW Helper
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P: 5,003
Quote Quote by nutan123 View Post
1. The problem statement, all variables and given/known data

A thin conductor plate is in free space. Its conductivity is finite and thickness is approaching zero. Relate the tangential electric field in either side of the conductor. Repeat for tangential magnetic field. How are electric and magnetic fields related.
Are you given any other information, such as the free charge density or free current density on the plate?

2. Relevant equations
Standard boundary conditions
[tex]\textbf{n}[/tex]*([tex]\textbf{h2}[/tex]-[tex]\textbf{h1}[/tex])=[tex]\rho[/tex]
[tex]\textbf{n}[/tex]*([tex]\textbf{e2}[/tex]-[tex]\textbf{e1}[/tex])=0
Those are not standard boundary conditions. Assuming [itex]\textbf{n}[/itex] represents the surface unit normal, [itex]\textbf{n}\cdot\left(\textbf{E}_2-\textbf{E}_1\right)[/itex] and [itex]\textbf{n}\cdot\left(\textbf{H}_2-\textbf{H}_1\right)[/itex] represent difference in the normal components of the fields....you are asked to relate the tangential components of the fields.

In any case, [itex]\textbf{n}\cdot\left(\textbf{H}_2-\textbf{H}_1\right)\neq\rho[/itex] (I assume [itex]\rho[/itex] is supposed to represent the free surface charge density?) and [itex]\textbf{n}\cdot\left(\textbf{E}_2-\textbf{E}_1\right)\neq 0[/itex] in general.


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