Chapter 3. Electric Flux Density, Gauss ’ s Law, and Divergence

1. Chapter 3. Electric Flux Density, Gauss’s Law, and Divergence • Electric Flux Density • Faraday: The total charge on the outer sphere is equal in magnitude to the charge placed on the inner sphere. 목원대학교 전자정보통신공학부 전자기학

2. Gauss’s Law • The electric flux passing through any closed surface is equal to the total charge enclosed by that surface. 목원대학교 전자정보통신공학부 전자기학

3. The application of Gauss’s Law 목원대학교 전자정보통신공학부 전자기학

4. Application of Gauss’s Law: Some Symmetrical Charge Distributions • How to use Gauss’s law to determine D if Q is known. • The solution is easy if we can choose a closed surface to satisfy two conditions. • Let us again consider a point charge Q at the origin of a spherical coordinate. • On the spherical surface, 목원대학교 전자정보통신공학부 전자기학

5. Second example : uniform line charge along z axis 목원대학교 전자정보통신공학부 전자기학

6. Two coaxial cylindrical conductors 목원대학교 전자정보통신공학부 전자기학

7. Application of Gauss’s Law: Differential Volume Element 목원대학교 전자정보통신공학부 전자기학

8. Divergence • The divergence of the vector flux density A is the outflow of flux from a small closed surface per unit volume as the volume shrinks to zero.=> positive divergence: source, negative divergence: sink • Maxwell’s First Equation (Electrostatics) 목원대학교 전자정보통신공학부 전자기학

9. The Vector Operator ∇ and The Divergence Theorem • The integral of the normal component of any vector field over a closed surface is equal to the integral of the divergence of this vector field throughout the volume enclosed by the closed surface. 목원대학교 전자정보통신공학부 전자기학