Question

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

Answer 1

From the symmetry o f the problem, the voltage across each capacitor, and charge on each capacitor in the absence of dielectric.

Now when the dielectric is filled up in one of the capacitors, the equivalent capacitance of the system,

and the potential difference across the capacitor, which is filled with dielectric,

So, as φ decreases 1/2(1 + ε) times, the field strength also decreases by the same factor and flow of charge,