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Question

A parallel plate air capacitor has capacitance C. Half of space between the plates is filled with di-electric di-electric constant K as shown in figure. The new capacitance is C. Then
970015_8a9c8626cfd74042a4466f0e89bfd40c.png

A
C=C[KK+1]
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B
C=C[2KK+1]
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C
C=2CK+1
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D
None of the above
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Solution

The correct option is A C=C[2KK+1]
The field with in the 1st media
E1=σϵ1
The field with in the 2nd media
E2=σϵ2
Potential Difference
V=E1d1+E2d2
=σϵ1d1+E2d2
=σ(d1ϵ1+d2ϵ2)
=QA(d1ϵ1+d2ϵ2)
where σ is the surface change density
σ=QA
The capacitance in the case,
C=QV=Ad1ϵ1+d2ϵ2=ϵ0Ad1K1+d2K2
where K is are the dielectric constant
ϵi=Kiϵ0
If K1=1,K2=K,e=ϵ0Aα1+d2K[d1=d2=d]
If K1=1,K2=1,e=ϵ0A2d=Kϵ0Ad(K+1)
e=e[2KK+1]

1441429_970015_ans_369ec4d50a854923a00cc36b4b906c5f.png

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