Formula for Solving Boundary Condition in EMFT

The Boundary Conditions on the electric and magnetic fields (i.e. relationships between the electric and magnetic fields on either side of a boundary) are important for understanding the behaviour of electromagnetic fields, We can drive these Boundary Condition from Maxwell’s equations. For Electric field Intensity: If the field in one region of dielectric medium ε1 is known then the field in adjacent region can be calculated using Boundary Condition. 

Case_1: Electric Field is Normal to the Boundary

                                   

                                       We Know that,

                            i.e for Normal Density,          D_n2 = D_n

For region having Charge on Boundary, 

Note:

1. Considered surface spread in both the region that’s why we apply single Gauss law Equation for analysis. If Boundary has a surface charge   than normal component of Density will be:
   
   
   
2. The Normal Component of flux density is continuous on both the side when there is no surface charge else discontinuous by an amount equal to surface charge density  .

 

Case_2: When Electric field is parallel to Boundary

            We know that,

• Tangential Component of Electric Field Intensity is Always Continuous.

• The Formula of Boundary Condition for both Electric and Magnetic Field is Summarized in the table.