Question

Boundary conditions for electric and magnetic fields

Answer 1

The differential forms of Maxwell's equations are used to solve for the field vectors provided the field quantities are single valued, bounded and continuous. At the media boundaries, the field vectors are discontinuous and their behaviors across the boundaries are governed by boundary conditions. The integral equations(eqn 5.26) are assumed to hold for regions containing discontinuous media.Boundary conditions can be derived by applying the Maxwell's equations in the integral form to small regions at the interface of the two media. The procedure is similar to those used for obtaining boundary conditions for static electric fields (chapter 2) and static magnetic fields (chapter 4). The boundary conditions are summarized as follows

Answer 2

there are four laundry conditions

1. tangential components of electric field intensity are continuous at the boundary
2. the normal components of electric flux density are discontinuous at the boundary by an amount equal to the surface charge density on the boundary.
3. the tangential component of magnetic field intensity are discontinuous at the boundary by an amount equal to surface current density on the boundary.

• the normal component of magnetic flux density are continuous at the boundary surface.