普通物理學甲下 ( A2) General Physics(A)(2) 台大物理 吳俊輝 Electricity II

Flux (used in Gauss Law)  The concept of flux – fluid flow across a surface. ( 通量 : 單位時間通過的量 )  Intuitively, it is the component of the fluid velocity that is normal to the area of interest, i.e. the flow across the area: flux

Gaussian surface  A Gaussian surface is a closed surface which we use to calculate the flux of E field.  Electric flux: the electric field has been given the “properties” of a fluid-flow field. This allows us to determine the properties of electric field more easily.  The total net electric flux across a Gaussian surface is 方向為由 Gaussian surface 內部朝外

Gauss’s Law where is the sum of all charges enclosed by the Gaussian surface.

Examples: choosing a Gaussian surface  Gauss’ Law can be applied to any closed surface:  e.g.:  高斯定律的用處：求電場，及 研究電荷系統的性質 …

1. Spherical Symmetry  From symmetry, we know that the electric field is the same at a given distance r from the center of the charge.  By Gauss Law, we have  The electric field points away from the charge center as we know from the area integral.  Coulomb’s Law

2. Charge on an isolated conductor  將電荷置於絕緣導體上時 …  電荷會分佈在導體的外表面 !!! By the Gauss Law: (a) electric field must be zero inside a conductor, otherwise the charges would flow. Therefore, excess charges must be on the conductor exterior. (b) electric field inside a conductor must be zero, therefore, no charge is on the inner surface!

3. Planar geometry and Gauss’ Law  Excessive + charge on a large planar conductor.  Let’s use Gauss’ Law:  Again, the symmetry dictates that E must point perpendicular away from the plane ( is charge per unit area).  Therefore, Again, the field points away from the plane from the area integration.

4. Cylindrical symmetry  A very long plastic wire with uniform charge per unit length  So the electric field with 1/r away from a long wire.

 Electrical potential: Electrical work (W E ), energy (U), and potential (V)  電荷在電場中移動時，電場會對其作功， 造成其位能的改變：  The unit of V: joule/coulomb (J/C) = volt (V).

Equipotential Surface  Surfaces of constant V (electric potential) 

Electron volt (eV)  能量的單位： joule (J), electron volt (eV).  1 eV = energy needed to move a particle with charge e across a potential difference of 1 V.  So

Some practical knowledge about electricity  Power P=IV  Current I=dq/dt : 1. AC: Alternating Current 2. DC: Direct Current  Ohm’s Law V=IR

Medical device - defibrillator  Energy is stored in a capacitor to stop fibrillation of heart attack patients (100kW of pulsed energy can be applied to a patient) Apply to patient

Exercise 1 ( 習題 1)  Ch 21: 25, 60, 83  Ch 22: 22, 41, 65, 87  Ch 23: 21, 29, 47, 81  Deadline: 3/6, 10:20AM