Chapter 7 Dielectrics: II Continuity Conditions at The interface Potential Energy Forces on Conductors in the presence of Dielectrics a Forces on dielectrics Displacement Current Frequency and Temperature dependence, Anisotropy
Chapter 7 Dielectrics: II ◼ Continuity Conditions at The Interface ◼ Potential Energy ◼ Forces on Conductors In The Presence Of Dielectrics ◼ Forces On Dielectrics ◼ Displacement Current ◼ Frequency and Temperature Dependence, Anisotropy
7.1 Continuity Conditions at the Interface Between Two Media At the interface between the two media, the quantities V, E, and d must satisfy certain boundary conditions 1. The potential v At the boundary btwn two media, V must be contin uous,otherwise aV/ar would be oo, and e would be For a charge distribution in a finite region the potential V is normally set to zero at infinity
2. The Normally Component of D (See Fig 7-1) Consider a short gaussian cylinder drawn about a bound- ary surface The cross-section area of the cylinder is s The boundary surface carries a free surface charge o Then the flux of d emerging from the flat cylinder is equal to the charge enclosed Thus the bdry condition of d is (DnI -Dn2
S D D Figure 7-1 Gaussian cylinder on the interface between two media I and 2. The difference D, I-D,, between the normal components of D is equal to the surfac density of free charge o
Examples If the boundary surface free charge of=0, the en m1=1m2, the normal component of d is continuous this is usu ally the case for two dielectric media If the boundary is between a conductor and a dielectric, D=0in the conductor, and Dn =of in the dielectric where o f is the free charge density on the surface of the conductor