EEE340Lecture 161 Solution 3: (to Example 3-23) Apply Where lower case w is the energy density

EEE340Lecture 162 Hence

EEE340Lecture 163 Example 3-24: Energy stored in a parallel plate capacitor Solution: +Q -Q

EEE340Lecture System of Bodies with Fixed Charges electrostatic Forces

EEE340Lecture 165 Angular displacement 2. System of conduction bodies with fixed potentials

EEE340Lecture 166 Example 3-26 Determine the force on the conduction plates of a charged parallel-plate capacitor. The plates have an area S and are separated in air by a distance x. Solution a)Fixed charges from Eq. (3-180b) Negative sign implies attractive force.

EEE340Lecture 167 b) Fixed potentials.

EEE340Lecture 168 Chapter 4: Solution of Electrostatic Problems 4-2: Poisson’s and Laplace’s equations. Using the differential form of Gauss’s law Plus (3.43) We obtain Or i.e. which is the Poisson equation. (3.98),(4.1) (4.3) (4.6)

EEE340Lecture 169 The Laplace operator rectangular cylindrical spherical (4.7) (4.8) (4.9)

EEE340Lecture 1610 Example 4-1: Parallel-plate capacitor Solution. Assume the potential within the two plates has no variation in the x and z directions, the Laplace equation reduces to Integrating over dy twice, we have The two constants of integration can be determined by two boundary conditions Hence Namely and (4.11) (4.12) (4.14) y 0 d

EEE340Lecture 1611 The E-field and surface charge density are And (4.15)