Que 12. Obtain an expression for capacitance of a parallel plate capacitor without a dielectric. A metal plate is introduced between the plates of a charged parallel plate capacitor. What is its effect on the capacitance of the capacitor?
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Explanation:
Let the two plates are kept parallel to each other separated be a distance d and cross-sectional area of each plate is A.
Electric field by a single thin plate E
′
=
2ϵ
o
σ
Total electric field between the plates E=
2ϵ
o
σ
+
2ϵ
o
σ
Or E=
ϵ
o
σ
Or E=
Aϵ
o
Q
Potential difference between the plates V=Ed
⟹ V=
Aϵ
o
Qd
Capacitance C=
V
Q
Thus we get capacitance of parallel plate capacitor C=
d
Aϵ
o
solution
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