Electromagnetic 1 Chapter 5 Steady electric currents Conduction currents : Drift motion of conduction electrons of holes in conductor or semicond. Electrolytic currents : Migration of positive or/negative ions. Convection currents : Motion of elections ions in vacuum. Kirchhoff’s voltage law : Electromotive force Kirchhoff’s current law : Conservation of charge Ohm’s law : V=IR

Electromagnetic Current Density & Ohm’s law 電荷流過 表面為 ：單位體積電荷 ：電荷流動之速度 ：電荷隨時間之改變率 (Volume) current density ， ： free charge per unit volume ： convection current density

Electromagnetic 3 Ex ： 5-1 負數 代回

Electromagnetic 4 求, 必須解 Poisson’s Equation * 同乘以 積分左式： 右式： child – langmuir law

Electromagnetic 5 * 多種載子 (e 、 p 、 ion…)  金屬導體  半導體 ( 電子與電洞 ) [point form] of ohm’s law 電路學 : ohm’s law

Electromagnetic 6 Point form ohm’s law Potential Difference of terminals is 與 結合 length cross-section Point form ohm’s law derive Ckt ohm’s law

Electromagnetic 7 Ex ： 5-2 Sol : Conductance (G) 電路學 a) 串聯 ( 電流一樣 ) b) 並聯 ( 電壓一樣 )

Electromagnetic Electromotive Force & Kirchhoff’s voltage Law static electric field ohm’s law The source of the nonconservative field Electric battery,……. Impressed electric field intensity Electromotive force V Inside source outsideinside outside

Electromagnetic 9 Ohm’s Law Charge cumulation Chemical action 推廣 k 個 R Kirchhoff’s voltage Law

Electromagnetic Equation of Continuity and Kirchhoff’s Current Law Principle of conservation of charge Current leaving the region = total outward flux of Divergence Theorem equation of continuity

Electromagnetic 11 Steady currents,, Kirchhoff’s current Law 其中 ： relaxation time Conductor 內

Electromagnetic Power Dissipation & Joule’s Low 單一原子 work Power drift velocity Total power : point functionPower density under steady-current Joule’s Law

Electromagnetic 13 dsdl A constant cross-section

Electromagnetic Boundary conditions for current density Steady current DifferentialIntegral

Electromagnetic 15 Ex ： 5-3

Electromagnetic 16 Steady current flows 2 lossy dielectrics 1 2

Electromagnetic 17 Ex 5-4 : static charge & steady current 同時存在 surface charge upper lower Interface surface charge

Electromagnetic Resistance Calculations capacitance ohm’s Law resistance

Electromagnetic 19 Ex ： 5-5

Electromagnetic 20 計算電阻 R 的步驟 1. 針對問題, 選擇適當座標系統。 2. 假設兩導體之電位差 V 。 3. 求出兩導體間的電場 。 4. 求總電流 5.

Electromagnetic 21 Ex ： 5-6 Cylindrical coordinate Laplace’s equFind total current 代入