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Unformatted text preview: ing them and the area they cover are exactly the same, they will have the same capacitance.” same “Capacitance will decrease because the distance over which the electric field acts will Capacitance decrease” decrease” Capacitance Capacitance Capacitance is defined for any pair of spatially separated conductors Q C≡ V How do we understand this definition ??? • Consider two conductors, one with excess charge = +Q and the other with excess charge = ­Q +Q d E V -Q • These charges create an electric field in the space between them • We can integrate the electric field between them to find the potential difference between the conductor • This potential difference should be proportional to Q • The ratio of Q to the potential difference is the capacitance and only depends on the geometry of the conductors 9 Example (done in Prelecture 7) First determine E field produced by charged conductors: +Q y d x E -Q σ E= ε0 What is σ ?? ?? Q σ= A A = area of plate Second, integrate E to find the potential difference V d d d Q V = − ∫ E ⋅ dy V = − ∫ (− Edy ) =E ∫ dy = d ε0 A 0 0 0 As promised, V is proportional to Q !! 12 Q Q C≡ = V Qd /(ε 0 A) ε0 A C= d C determined by geometry !! Question Related to Preflight +Q0 +Q Initial charge on capacitor = Q0 BB d -Q0 +Q1 Insert uncharged conductor into isolated capacitor Charge on capacitor now = Q1 d t -Q1 How is Q1 related to Q0 ?? A. B. C. 14 Q1 < Q0 Q1 = Q0 Q1 > Q0 Plates not connected to anything—different from Prefl 10 CHARGE CANNOT CHANGE !! Where to S...
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