This unit provides an introduction to numerical methods for s

This unit provides an introduction to numerical methods for solving maths-related problems on computers. Topics covered include an introduction to Matlab ...

1. The Boundary Conditions of Electric Field, Electric Potential and Dispacement Current Presented to: Presented By:

2. Boundary conditions are the constraints imposed on electric and magnetic fields at the interfaces between different media or regions. Introduction These conditions ensure the continuity of fields and their derivatives across boundaries, allowing for the solution of Maxwell's equations in various physical scenarios.

3. Boundary conditions play a crucial role in determining the behavior of electric and magnetic fields at interfaces. Why Boundary Conditions? They enable the prediction of phenomena such as reflection, refraction, and transmission of electromagnetic waves, as well as the behavior of charges and currents in various physical systems Boundary conditions are fundamental principles in electrodynamics, governing the behavior of electric and magnetic fields at interfaces.

4. Consider the field existing in a region that consists of two different dielectrics characterized by . The fields and in media 1 and media 2 can be decomposed as Consider the closed path abcda shown in the below figure. By conservative property   Boundary Conditions

5. Boundary Conditions To study the boundary conditions, both the vectors are resolved into two components ( i ) Tangential to the boundary (Parallel to boundary) (ii) Normal to the boundary (Perpendicular to boundary) To study Tangential component, C onsider a rectangular path and gaussian surface to determine the boundary conditions As we know,  

6. Boundary Conditions At the boundary,  

7. Boundary Conditions The tangential components of Electric field intensity are continuous across the boundary. Since , the above equation can be written as Now, for potential V as we know, =  

8. Boundary Conditions Now, to find normal components, Consider a cylindrical Gaussian Surface as shown. According to Gauss's law  

9. Top Bottom Lateral At the boundary, , So only top and bottom surfaces contribute in the surface integral The magnitude of normal component of is and For top surface   Boundary Conditions

10. For bottom surface For Lateral surface   Boundary Conditions

11. Boundary Conditions In vector form, For perfect dielectric, The normal components of the electric flux density are continuous across the boundary if there is no free surface charge density.