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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.

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a

6×107V

b

3×107V

c

4×107V

d

2×107V

answer is A.

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Detailed Solution

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=ε0Ad+ε0A2d=32ε0AdPotential of central plate,v=QC=Q2d3ε0A=1×2×2×10−33×8.85×10−12×2.5≈6×107

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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.