A simple capacitors related question

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SUMMARY

The discussion centers on the capacitance of two identical capacitors with parallel plates, each containing a metal insert of thickness d/3 positioned between the plates. The key difference is that in one capacitor, the metal insert is connected to the upper plate, while in the other, it is not. The conclusion drawn is that the capacitance is greater in the capacitor with the connected metal insert due to the influence of the electric field and charge distribution, which enhances the overall capacitance.

PREREQUISITES
  • Understanding of capacitor fundamentals, including capacitance and electric fields.
  • Knowledge of parallel plate capacitor configurations.
  • Familiarity with the effects of dielectric materials on capacitance.
  • Basic principles of electrical connections and their impact on circuit behavior.
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Homework Statement


Consider two identical capacitors with parallel plates (the distance between the plates is (d). In each of them a metal (thickness d/3, surface equal to the plates surface) is placed right in between the plates. In one of them a metal part is connected to the upper plate, an in the other one its not connected.

The capacity is
1) greater in the capacitor with connection
2) vice versa
3) its equal
4) we can't tell (why?)


The Attempt at a Solution



I think that its greater in the one with connection
 
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