A parallel plate capacitor of area A has the region between the plates filled wi

Question

A parallel plate capacitor of area A has the region between the plates filled with two
different dielectrics and a conductor as shown. Assume a charge Q is placed on the
plates.
a) Find the electric field in all three regions.
b) Find the capacitance
c) Find the energy stored in the field

A parallel plate capacitor of area A has the region between the plates filled with two different dielectrics and a conductor as shown. Assume a charge Q is placed on the plates. a) Find the electric field in all three regions. b) Find the capacitance c) Find the energy stored in the field

Explanation / Answer

The capacitance of a parallel plate capacitor of plate area A and plate separation d with vacuum inbetween is given by;

C0=e0A/d

Suppose Q are the charges on the capacitor plates which prou=duce a uniform electric field E0.

When a dielectric slab of thickness t<d is introduced between the plates, the molecules in the slab gets polarized in the direction of E0.

The electric polarization vector E0 induces an electric field Ep opposite to E0.

Therefore, effective field inside dielectric is E=E0-Ep

Outside dielectric, field remains E0 only.

Therefore potential difference between two plates;

V=E0(d-t)+Et

But,

E0/E=k

So,

E=E0/K

So,

V=E0(d-t)+E0 t/k

V=E0{d-t+t/k}

As E0=s/e=Q/Ae0

So,

V={Q/Ae0}*{d-t+t/k}

Capacitance of the capacitor with dielectric inbetween is;

C=Q/V=Ae0/{d-t+t/k}=e0A/d-t(1-1/k)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.