Consider a parallel plate capacitor with rectangular plates and a sheet of metal

Question

   Consider a parallel plate capacitor with rectangular plates and a sheet of metal of thickness a. The
dimensions of the capacitors are given in [mm]. Let x be the length of the metal plate that is
inserted between the capacitor plates. Let +Q and -Q be the charges [fC] on the plates of the capacitor.
a) Find the capacitance Co and the energy Uo stored in the capacitor before the metal sheet is inserted.
b) Find the capacitance C and the energy U stored in the capacitor after insertion of the metal sheet as
function of x.
c) Find the force on the metal sheet ? Which direction does it tend to move the metal sheet ?

Explanation / Answer

(a) Co= (o A)/d =o (L*w)/b.

      U0= (Q^2)/2Co = (Q*Q)/2Co....where Co has the value as calculated above!

(b) after insertion of themetal sheet...there are three capacitors..which may be visualised as..(1) first face of capacittor and metal (2) second faceof capacitor and metal sheet (3) remaining bottom surface of the plates of capacitor.

the first two capacitor are in series and the third capacitor is in parallel with the series combination of first two!!! hence u may calculate the capacitance(final).

again use U= qi^2/2ci..where i= 1,2,3...u may calculate the respective charge as is constant on the surface of the capacitor plates and the facing metal sheets have equal and opposite charge!!!

(c) F= - U/x..where u calculated the U above..and the force is attracting in nature..which u can easily observe from the above formula...calculate it and if u have any problem in solving then u may comment here.!!!!

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