A capacitor made of two parallel plates, each of area A and separation d is charged by an external DC source. show that during charging, the displacement current inside the capacitor is the same as the current charging the capacitor.
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ANSWER:
TD=ε0dμEdtlet the altering emf charging the plates of capacitor be E=E
0
sinωt
charge on the capacitor q=EC=CE
0
sinωt
I=
dt
dq
=
dt
d
(CE
0
sinωt)=ωCE
0
cosωt=I
0
cosωt(whereI
0
=ωCE
0
)
Displacement current
I
D
=ε
0
dt
dψ
E
=ε
0
A
dt
dE
=ε
0
A
dt
d(
ε
0
A
q
)
=ε
0
A
dt
d
(
ε
0
A
CE
0
sinωt
)
=
dt
d
(CE
0
sinωt)=ωCE
0
cosωt=I
0
cosωt
Thus the displacement current inside the capacitor is the same as current charging the capacitor.
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