(ne08) 電勢和電場 Potential & Fields


Pre-amble

  1. MS Electrostatics 1 results....
  2. Review: Remembering signs and directions:
    Think: +ve ≡ 男 -ve ≡ 女
    E-field direction: 男抓女 NOT 女抓男
    Test Charge (q):勇敢的男性
    Potential (V): 男(山) 女(洞)
    V and q:两男吵架,两女吵架,男进女和平

Key Points (assumption: charge conservation)

Force and Work
$$ W = \Delta U + \Delta K = \int \mathbf {\vec F } \cdot d \, \mathbf {\vec s} = q \int \mathbf {\vec E } \cdot d \, \mathbf {\vec s} $$
Potential and Fields
IntegrateDifferentiate
$$ \Delta V = \int \mathbf {\vec E } \cdot d \, \mathbf {\vec s} \,\, [1] $$ $$ \mathbf {\vec E } = \mathbf \nabla \, V \,\, [2] $$

Application:

電池 Batteries (emf)$$ \Delta V_{bat} = W_{chem} / q = \mathscr E $$

Capacitors $$ \mathbf {\vec E } = Q {1 \over {\epsilon_o A}} \hat i \, \rightarrow \, \Delta V = Q {d \over {\epsilon_o A}} \, \rightarrow \, \Delta V = {Q \over C} $$
$$Parallel: C_{eq} = \Sigma C_i $$$$ Series: C_{eq}^{-1} = \Sigma C_{i}^{-1} $$
Energy Storage$$ \Delta U = \frac{1}{2C} \, Q^2 = \frac{1}{2} C \Delta V^2 = \frac{1}{2} {\epsilon_o A \over d} (Ed)^2 = \frac{1}{2} \epsilon_o (Ad) E^2 $$

Kirchoff's Law 1:$$ \Delta V_{closed \, loop} = \Sigma \Delta V_i = 0 $$

Lecture Power Points: Knight Chapter 29


Capacitor Lab
Capacitance

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