Lecture 9: Capacitance and Capacitors The interior of a Sony Walkman

Physics for Scientists and Engineers Chapter 24: Electrostatic Energy and Capacitance Copyright © 2004 by W. H. Freeman & Company Paul A. Tipler Gene Mosca Fifth Edition

Learning Objectives To introduce the concept of capacitance, C To provide a definition for the C of a conductor To calculate C of ideal capacitors

The Importance of Capacitors: (a) They store potential energy in the E-field (b) Many applications Examples include: (i) use in electronics (ii) flash units of cameras (iii) pulsed lasers (iv) computer keyboard

Capacitance for Charge Q placed on a conductor changes the conductor’s potential by V Define the capacitance C of the conductor by the equation Unit of C - coulomb volt -1 - farad (F)  Q

Example: an isolated conducting sphere of radius a and carrying a charge Q So A sphere of radius 9  10 9 m (more than 10 3  that of the Earth) would have a capacitance of about 1 farad. Common capacitors in use: pF-  F

Earthing a Radius b Consider two conducting spheres Charge q

The two spheres acquire the same potential qaqa qbqb Earthing

Same potential means Total charge is constant Thus

Important Conclusion Earthed isolated charged bodies share their charge with the Earth - effectively lose that charge. The bodies and the Earth acquire a common potential - called zero of potential.

The potential of the earth does not change Because a is very Large Similar to the use of sea level as a reference for height

Capacitors It is a system of high capacitance, designed for the storage of separated positive and negative charges A capacitor is achieved by moving charge from one conductor to another

It is a measure of the ability of a capacitor to store energy Capacitance of a Capacitor Defined by:

5 Given that : What is

Calculation of Capacitance 3 geometries - planar, cylindrical, and spherical Procedure Calculate the change of V Apply C = Q/V

(a) The Parallel Plate Capacitor We will ignore any fringing effects

d  Gauss’s Law: Potential difference between the two plates: Ed

The symbol of a capacitor in electric circuits

If the voltage across a parallel plate capacitor is doubled, its capacitance: (a)Doubles (b)Drops by Half (c)Remains the same

If the charge on an isolated spherical conductor is doubled, its capacitance: (a)Doubles (b)Drops by Half (c)Remains the same

(b) A Long Cylindrical Capacitor (co-axial cable)

What is the capacitance per unit length? This is important in determining the transmission characteristics of the cable.

Choose a cylindrical Gaussian surface rbrb rara

(c) A Spherical Capacitor

r a r b Appropriate Gaussian surface is a sphere concentric with, and between, the conducting spheres +Q+Q -Q-Q

Hence or Therefore

The symbol for spherical capacitor

Review and Summary Procedure for calculating the capacitance of a capacitor Calculate the E-field (e.g. use Gauss’s Law) Use Followed by

Parallel plates capacitor Cylindrical capacitor Spherical capacitor An isolated sphere

Some Capacitances Capacitor TypeCapacitance Parallel Plate Cylindrical Spherical Isolated Sphere

Capacitors