Derive the equation for the capacitance of a parallel plate capacitor
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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
.','.
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