Pre-amble: Remembering signs and directions:
| Think: | +ve ≡ 男 | -ve ≡ 女 | 
|
| E direction: | 男抓女 NOT 女抓男 | ||
| Test 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 1. Potentials & Fields
Executive Summary: Their Relationship (assumption: charge conservation)
| ΔU + ΔK = W + Q (particle: q, m) | |
|---|---|
| $$ W_{gravity} = \int \mathbf {\vec F_g } \cdot d \, \mathbf {\vec s} = m \int \mathbf {\vec G } \cdot d \, \mathbf {\vec s} \,\,\,(system: particle) $$ | |
| $$ \Delta U_{gravity} = - \int \mathbf {\vec F_g } \cdot d \, \mathbf {\vec s} = - m \int \mathbf {\vec G } \cdot d \, \mathbf {\vec s} \,\,\,(system: particle + earth) $$ | |
| $$ W_{elec} = \int \mathbf {\vec F_e } \cdot d \, \mathbf {\vec s} = q \int \mathbf {\vec E } \cdot d \, \mathbf {\vec s} \,\,\, (system: particle)$$ | |
| $$ \Delta U_{elec} = - \int \mathbf {\vec F_e } \cdot d \, \mathbf {\vec s} = - q \int \mathbf {\vec E } \cdot d \, \mathbf {\vec s} \,\,\, (system: particle + earth)$$ | |
| Potential and Fields | |
| Integrate | Differentiate |
| $$ \Delta V = - \int \mathbf {\vec E } \cdot d \, \mathbf {\vec s} \,\, [1] $$ | $$ \mathbf {\vec E } = - \mathbf \nabla \, V \,\, [2] $$ |
| Kirchoff's Law 1: | $$ \Delta V_{closed \, loop} = \Sigma \Delta V_i = 0 $$ |
Lecture Power Points: Knight Chapter 26 Part 1
KEY 2. Sources of Electric Potential
| Van De Graaff Generator7', (in depth physics)15' Δ Vvdg ~ 100,000V |
| $$Battery \quad \Delta V_{bat} = W_{chem} / q = \mathscr E \,\,\, (emf) $$ |
| $$Capacitor \quad \Delta V_{cap} = Q / C $$ |
KEY 3. Application: Capacitors
Executive Summary
| $$ \mathbf {\vec E } = Q {1 \over {\epsilon_o A}} \hat i \, \rightarrow \, \Delta V = Q {d \over {\epsilon_o A}} \, \rightarrow \, \Delta V = {Q \over C} $$ | |
|---|---|
| $$Parallel: C_{eq} = \Sigma C_i $$ | $$ Series: C_{eq}^{-1} = \Sigma C_{i}^{-1} $$ |
| Energy Storage | $$ \Delta U = \frac{1}{2C} \, Q^2 = \frac{1}{2} C \Delta V^2 = \frac{1}{2} {\epsilon_o A \over d} (Ed)^2 = \frac{1}{2} \epsilon_o (Ad) E^2 $$ |
