Adding a Dielectric to a Non Electrically Isolated Capacitor (11:11)
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This video examines what happens when a dielectric is added to a parallel plate capacitor that is not electrically isolated, meaning it is connected to a constant power supply that holds the electric potential difference across the plates constant, rather than the charge. Because the dielectric constant κ of any material other than a vacuum is greater than 1, and the plate area and separation stay fixed, the capacitance increases when the dielectric is added. Since capacitance equals charge divided by electric potential difference, and the potential difference is held constant, the net excess charge on each plate must increase to match. Deriving the equation for the electric field between ideal parallel plates, E = Q/(κε₀A), shows that the electric field itself remains constant even as the charge increases, because the field's increase from more charge is exactly canceled by its decrease from the larger dielectric constant in the denominator. This is explained physically by recognizing that the net field equals the field caused by the increased charge minus the induced field caused by the polarized dielectric, and the two increase together, leaving the net field unchanged.
Chapters: 0:00 Introduction 1:38 Constant Potential Difference Capacitor 2:08 Capacitance Increases 2:54 Charge on the Plates Increases 4:29 Electric Field Remains Constant 5:09 Deriving the Electric Field Equation 6:35 Why the Electric Field is Constant 7:46 The Induced Electric Field 10:00 Summary
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