20075ee1_1_HW6

20075ee1_1_HW6 - CHAPTER 6. 6.1. Atomic hydrogen contains 5...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CHAPTER 6. 6.1. Atomic hydrogen contains 5 . 5 10 25 atoms/m 3 at a certain temperature and pressure. When an electric field of 4 kV/m is applied, each dipole formed by the electron and positive nucleus has an effective length of 7 . 1 10 19 m. a) Find P: With all identical dipoles, we have P = Nqd = (5 . 5 10 25 )(1 . 602 10 19 )(7 . 1 10 19 ) = 6 . 26 10 12 C / m 2 = 6 . 26 pC / m 2 b) Find r : We use P = e E , and so e = P E = 6 . 26 10 12 (8 . 85 10 12 )(4 10 3 ) = 1 . 76 10 4 Then r = 1 + e = 1 . 000176 . 6.2. Find the dielectric constant of a material in which the electric ux density is four times the polarization. First we use D = E + P = E + (1 / 4) D . Therefore D = (4 / 3) E , so we identify r = 4 / 3 . 6.3. A coaxial conductor has radii a = 0 . 8 mm and b = 3 mm and a polystyrene dielectric for which r = 2 . 56. If P = (2 / ) a nC / m 2 in the dielectric, find: a) D and E as functions of : Use E = P ( r 1) = (2 / ) 10 9 a (8 . 85 10 12 )(1 . 56) = 144 . 9 a V / m Then D = E + P = 2 10 9 a 1 1 . 56 + 1 = 3 . 28 10 9 a C / m 2 = 3 . 28 a nC / m 2 b) Find V ab and e : Use V ab = Z . 8 3 144 . 9 d = 144 . 9ln 3 . 8 = 192V e = r 1 = 1 . 56 , as found in part a . c) If there are 4 10 19 molecules per cubic meter in the dielectric, find p ( ): Use p = P N = (2 10 9 / ) 4 10 19 a = 5 . 10 29 a C m 1 6.4. Consider a composite material made up of two species, having number densities N 1 and N 2 molecules / m 3 respectively. The two materials are uniformly mixed, yielding a total number density of N = N 1 + N 2 . The presence of an electric field E , induces molecular dipole moments p 1 and p 2 within the individual species, whether mixed or not. Show that the dielectric constant of the composite material is given by r = f r 1 +(1 f...
View Full Document

This homework help was uploaded on 04/01/2008 for the course EE 1 taught by Professor Joshi during the Fall '08 term at UCLA.

Page1 / 4

20075ee1_1_HW6 - CHAPTER 6. 6.1. Atomic hydrogen contains 5...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online