Capacitor Electric Field Derivation (9:57)
We already derived the capacitance equation for a parallel plate capacitor, C = κε₀A/d. In this video, we use that capacitance equation, combined with the definition of capacitance, C = Q/ΔV, and the relationship between electric potential difference and electric field in a uniform field, ΔV = Ed, to derive the capacitor electric field equation: E = Q/(κε₀A). Then we apply that capacitor electric field equation to a homemade aluminum-foil-and-printer-paper parallel plate capacitor to solve for both the electric field's magnitude and the number of excess charge carriers on each plate.
Chapters:
0:00 Intro, and Reviewing Capacitance
0:42 Deriving the Electric Field Equation
2:54 Example Problem: Setting Up the Knowns
4:16 Part (a): Solving for the Electric Field
6:28 Part (b): Solving for the Number of Excess Charges
8:38 Why Is the Current Zero?
Chapters:
0:00 Intro, and Reviewing Capacitance
0:42 Deriving the Electric Field Equation
2:54 Example Problem: Setting Up the Knowns
4:16 Part (a): Solving for the Electric Field
6:28 Part (b): Solving for the Number of Excess Charges
8:38 Why Is the Current Zero?
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- Thank you to Christopher Becke, Nick Gillies, and Julie Langenbrunner for being my Quality Control Team for this video.