Physics 39 Capacitors (17 of 35) Energy Stored on a Charged Capacitor 2

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In this video I will calculate the energy stored when a dielectric is inserted into a capacitor (Battery will be removed after the capacitor is charged.).

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Why do we know or assume that E initial will be equal to E final? Considering right-most equations, wouldn't E final be E initial times k?

shent
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Where go potential energy after inserting dielectric into a capacitor without battery source?

RiaziMohandesi