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Question

The capacitance of a capacitor becomes 4/3 times its original value if a dielectric slab of thickness t=d/2 is inserted between the plates (d is the separation between the plates). What is the dielectric constant of the slab?

Solution
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The capacitance without dielectric is C=Aϵ0d.
When the dielectric slab of thickness t=d/2 and dielectric constant k is inserted between the plates, the capacitance becomes
C=Aϵ0dt(11k)=Aϵ0(dd2+d2k)
now , C=(4/3)CAϵ0(dd2+d2k)=(4/3)Aϵ0d
or 112+12k=43
or 2+2k=3k=2

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