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A parallel-plate capacitor has capacitance CO=8.00pF when there is air between the plates. The separation between the plates is 1.50mm. (a) What is the maximum magnitude of charge Q that can be placed on each plate if the electric field in the region between the plates is not to exceed 3.00×104V/m? (b) A dielectric withK=2.70 is inserted between the plates of the capacitor, completely filling the volume between the plates. Now what is the maximum magnitude of charge on each plate if the electric field between the plates is not to 3.00×104V/m?

Short Answer

Expert verified

(a)The maximum magnitude of the charge that can be placed on each plate is 0.36nC .

(b) The charge when a dielectric material with a dielectric constant is inserted between the two plates is 0.97nC

Step by step solution

01

The formula of the magnitude of the maximum charge on each plate and the charge between the plates when a dielectric material is inserted

Qo=CoV_____________1

whereQo is the initial charge,Co is the initial capacitance and V is the potential difference between the two plates.

role="math" localid="1664255788557" V=Eod_____________2

where V is the potential difference between the two plates,Eo is the electric field and d is the distance between the two plates

C=KCo_____________3

whereCo is the initial capacitance, Cis the capacitance with the dielectric material and K is the dielectric constant

according to equation (1)

Q=CV

using equation (3)

Q=KCoV_____________4

where, Q is the charge when a dielectric material is inserted between the two plates, K is the dielectric constant

02

The maximum magnitude of charge that can be placed on each plate.

(a)

We are given

the initial capacitance of a capacitor Co=8.00pF=8.00×10-12F

the separated distance between the two plates is d=1.50mm=0.0015mthe electric field without a dielectric material.

using equation, (2)

the potential difference between the two plates

role="math" localid="1664255530284" V=Eod=3.00×104V/m0.0015m=45.0V

putting value of V in equation (1)

The charge on the two parallel plates

Qo=CoV=8.00×10-12F45.0V=0.36×10-9C=0.36nC

Therefore, the maximum magnitude of the charge that can be placed on each plate is 0.36nC.

03

The charge between the plates when a dielectric constant is inserted

Using equation4

The charge Q when a dielectric material with a dielectric constant is inserted between the two plates

Q=KC0V=2.708.00×10-12F45.0V=0.97×10-9C=0.97nC

Therefore, the charge Qwhen a dielectric material with a dielectric constant is inserted between the two plates is 0.97nC .

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