An isolated large-plate capacitor, not connected to anything,originally has a po

Question

An isolated large-plate capacitor, not connected to anything,originally has a potential difference of 1500 volts with an air of3mm. Then a plastic slab of 1mm thick, with electric constant 8, isinserted halfway into the middle of the air gap as shown. Calculatethe potential difference between the plates. An isolated large-plate capacitor, not connected to anything,originally has a potential difference of 1500 volts with an air of3mm. Then a plastic slab of 1mm thick, with electric constant 8, isinserted halfway into the middle of the air gap as shown. Calculatethe potential difference between the plates.

Explanation / Answer

Charge must remain the same, so    Q =CV   initially   .           Q = A V / d   =    A 1500 / 3   =   A500 . In the final state, you have two capacitors: one ofthickness 1mm with dielectric of 8 and one withthickness of 2mm and air. . with dielec    Q = k A V1 / d = 8 * AV1 / 1   =   8 V1A . with air       Q = AV2 / d =   V2 A /2   =    0.5 V2 A . Set first two equal:       8 V1 A = A500          V1 = 62.5 . Set first and thirdequal       0.5 V2A = A500           V2 = 1000 .     Total new potential diff =   1000 + 62.5   =    1062.5volts

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