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Question

A parallel-plate capacitor has the air as a medium between its plates and its capacitance is C. A slab of the dielectric constant K is introduced so as to fill the left half of space of the capacitor, as shown. What is the new capacitance of the capacitor?
199421_c89c3bb2208e4d14a4b87a5749d304f1.png

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Solution

When the medium is air, the capacitance, C=Aϵ0d where A be the area of plates and d be the separation between plates.
When slab is introduced, the whole capacitors will break into two capacitors C1(with slab) and C2 (without slab) and they are in parallel.
Here, C=(A/2)Kϵ0d=KC/2
and C2=(A/2)ϵ0d=C/2
Thus, new capacitance is Cp=C1+C2=KC/2+C/2=C2(K+1)


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