Thin conducting plate boundary conditions

[nutan123]

Homework Statement

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.

Homework Equations

Standard boundary conditions
$$\textbf{n}$$*($$\textbf{h2}$$-$$\textbf{h1}$$)=$$\rho$$
$$\textbf{n}$$*($$\textbf{e2}$$-$$\textbf{e1}$$)=0

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.

 

[gabbagabbahey]

Homework Statement

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?

Homework Equations

Standard boundary conditions
$$\textbf{n}$$*($$\textbf{h2}$$-$$\textbf{h1}$$)=$$\rho$$
$$\textbf{n}$$*($$\textbf{e2}$$-$$\textbf{e1}$$)=0

Those are not standard boundary conditions. Assuming $\textbf{n}$ represents the surface unit normal, $\textbf{n}\cdot\left(\textbf{E}_2-\textbf{E}_1\right)$ and $\textbf{n}\cdot\left(\textbf{H}_2-\textbf{H}_1\right)$ represent difference in the normal components of the fields...you are asked to relate the tangential components of the fields.

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