Two earthed and parallel conducting plates having same area, A $$=$$ $$2.5$$ $$m2$$ are separated by $$6$$ mm. A third identical plate is introduced into the system parallel with the earlier plates at a distance of $$4$$ mm from one plate as shown in the figure. If this plate is given a charge of $$1C$$, then calculate the potential of the central plate.

Question

Two earthed and parallel conducting plates having same area, A $$=$$ $$2.5$$ $$m2$$ are separated by $$6$$ mm.  A third identical plate is introduced into the system parallel with the earlier plates at a distance of $$4$$ mm from one plate as shown in the figure. If this plate is given a charge of $$1C$$,  then calculate the potential of the central plate.

Infinity Learn · Accepted Answer

The plates $$1$$ and $$2$$ will form on capacitor and plates $$2$$ and $$3$$ will form another capacitor. These two capacitors are in parallel. Their effective capacitance $$isC=$$ε$$0Ad+$$ε$$0A2d=32$$ε$$0AdPotential$$ of central plate,$$v=QC=Q2d3$$ε$$0A=1$$×$$2$$×$$2$$×$$10$$−$$33$$×$$8.85$$×$$10$$−$$12$$×$$2.5$$≈$$6$$×$$107$$

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