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Chapter 26

Capacitance and Dielectrics

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Outline

Definition of capacitance (26.1) Calculating capacitance (26.2)

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A capacitor A capacitor: Consider two

conductors carrying charges of equal magnitude and opposite sign. Such a combination of two conductors is called a capacitor. Consists of two conductors separated

by an insulator (a nonconducting material or a dielectric).

The conductors are called the plates. A potential difference exits between

the conductors due to the presence of the charges.

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Charging of a parallel-plate capacitor

A capacitor is a device that stores energy (electric potential energy) as ell as charge.

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Capacitance C Experiments show that the quantity of charge

Q on a capacitor is linearly proportional to the potential difference between the conductors; Q = C V.

Capacitance C Q/V Q: magnitude of the charge on either conductor V: magnitude of the potential difference between

the conductors C is always positive; C is constant for a given

capacitor; C is a measure of a capacitor’s ability to store charge.

SI units for capacitance: farad (F); 1 F = 1C/V Other units: F (10-6 F) and pF (10-12 F)

Quiz: A 4 pF-capacitor is connected to a 9-V battery. Q = ?

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Calculating capacitance: parallel-plate capacitor

Example 1: Find the capacitance of a parallel-plate capacitor of area A and separation distance d. Answer: C = 0A/d The capacitance of a

parallel-plate capacitor is proportional to the area of its plates and inversely proportional to the plate separation.

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A real-world application: computer keyboard button

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Quick Quiz A parallel plate capacitor of capacitance C0 has

plates of area A with separation d between them. When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates. The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery. After the plates are 2d apart, the magnitude of the charge on the plates and the potential difference between them are

a. (1/2)Q0, (1/2)V0 b. (1/2)Q0, V0 c. Q0, V0 d. 2Q0, V0 e. 2Q0, 2V0

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Calculating capacitance: cylindrical capacitor

Example 2 (26.2): A solid cylindrical conductor of radius a and charge Q is coaxial with a cylindrical shell of negligible thickness, radius b>a, and charge –Q. Find the capacitance of this cylindrical capacitor if its length is l.

Answer: abk

lC

e /ln2

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HomeworkShow detailed solution, work, and reasoning for all problems.

1. A parallel-plate capacitor has plates of area 3.45 x 10-

4 m2. What plate separation is required if the capacitance is to be 1330 pF? Assume the space between the plates is filled with air.

2. A parallel-plate capacitor filled with air has plates of area 0.0066 m2 and a separation of 0.45 mm. (a) Find the magnitude of the charge on each plate when the capacitor is connected to a 12-V battery. (b) Will your answer to part (a) increase, decrease, or stay the same if the separation between the plates is increased? Explain. (c) Calculate the magnitude of the charge on the plates if the separation is 0.90 mm.