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Electric Capacitance, Energy of an Electric Field

Problem 3.102

Two parallel-plate air capacitors, each of capacitance \(C\), were connected in series to a battery with emf \(\mathscr{E} .\) Then one of the capacitors was filled up with uniform dielectric with permittivity \(\varepsilon\). How many times did the electric field strength in that capacitor decrease? What amount of charge flows through the battery?

Reveal Answer
 3.102. The strength decreased 1/2(ε+1) times; q==1/2CE(ε−1)/(ε+1)\begin{aligned} &\begin{array}{llll} \text { 3.102. The strength decreased } & 1 / 2(\varepsilon+1) & \text { times; } & q= \end{array}\\ &=1 / 2 C \mathscr{E}(\varepsilon-1) /(\varepsilon+1) \end{aligned}
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