The plates of an air-filled parallel-plate capacitor each have area2x10 3 cm 2 a

Question

The plates of an air-filled parallel-plate capacitor each have area2x103cm2 and are 1 cm apart. Thecapacitor is connected to a power supply and charged tom apotential difference of Vo=3kV. The capactiro is thendisconnected from the power supply without any charge being lostfrom its plates. After the capacitor is disconnected, a sheet ofinsulating plastic material is inserted between the plates,completely filling the space between them, When this is done, thepotential difference between the plates decreases to 1kV, while thecharge remains constant.
(a) What is the capacitance of the capacitor before the dialectricis inserted
(b)What is the charge on each of the plates
(c)What is the capacitance of the capcitor after the dialectric isinserted
(d)What is the dialectric constant of the plastic
(e)What is the electric field between the plates before andafter the dielectic is inserted

Explanation / Answer

The plates of an air-filled parallel-plate capacitor each have area2x103cm2 and are 1 cm apart. Thecapacitor is connected to a power supply and charged tom apotential difference of Vo=3kV. The capacitor is thendisconnected from the power supply without any charge being lostfrom its plates. After the capacitor is disconnected, a sheet ofinsulating plastic material is inserted between the plates,completely filling the space between them, When this is done, thepotential difference between the plates decreases to 1kV, while thecharge remains constant. (a) What is the capacitance of the capacitor before the dilectricis inserted Co=Ao/d=2x103*10-4*8.85*10-12/1*10-2=17.7*10-11F=177pF (b)What is the charge on each of the plates q=cV=177*10-12*3000=531nanoCoulomb (c)What is the capacitance of the capcitor after the dialectric isinserted C1=q/V=531nanoCoulomb/1000=531pF (d)What is the dielectric constant of the plastic k=C1/C0=3 (e)What is the electric field between the plates before andafter the dielectic is inserted before E=V/d=3000/1*10-2=300000V/m after E=1000/1*10-2=100000V/m

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