A dielectric slab of thickness 6cm is placed between the plates of a parallel plate capacitor. If the distance between plates is reduced by 4cm, the capacity of the capacitor remains the same. Find the dielectric constant of the medium.
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Correct option is D)
for a parallel plate capacitor
C = ε K A / d
It is possible that we have air/vacuum and then a medium in between the parallel plates. Initially there is a medium of dielectric constant K and of thickness d.
Let K1 be the dielectric constant of the slab.
let d1 be the thickness of slab = 6cm.
Formula for capacity with multiple media in between the plates is
C = ε A / [ d1/K1 + d2 / K ]
total gap = d1 + d2 = d + 4 cm => d2 = d + 4 cm - 6 cm = d - 2
d / K = d1/ K1 + d2 / K
d/ K = 6 / K1 + (d-2)/K
d - (d-2) = 6 K / K1
K1 = 3 K
If there was air originally in between the plates, K = 1, then answer is 3.
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