8/13/2019 Problems on Electrostatics

1/3

Page 1 of 3

EE101 Engineering Electromagnetics Winter 20141/15/14Homework #2

Due: Wednesday Jan 22 8:00 AM

Hand in to the TA at beginning of class. No late homework is accepted (see grading policy posted on eeweb).

6e=6 th edition, 5e = 5 th edition

Problem #1 (10 points) Find the capacitance per unit length of the coaxial line shown inFig. 4-25 in Ulaby.

Problem #2 (30 points) Coaxial capacitor

Consider a piece of coaxial cable of length l with two dielectric layers with permittivities and . You may consider the inner conductor (radius a) and the outer conductor shell (radius 4 a) to

be perfect conductors.

(a) What is the capacitance C between the inner and outer conductors? (Your answer should be in terms of only geometric and material parameters.)

(b) Consider that the dielectric layers are lossy with conductivities 1 and 2 respectively.What is the resistance R between the inner and outer conductors?

8/13/2019 Problems on Electrostatics

2/3

Page 2 of 3

Problem #3 (30 points) Poissons Equat ion and Dielectric relaxation

Consider a leaky parallel-plate capacitor with area A, thickness d , and a lossy dielectric with permittivity and non-zero (but small) Ohmic conductivity . At time t = 0, there is a freevolume charge density ( x,t =0) = 0 x/d inside the dielectric (0< x

8/13/2019 Problems on Electrostatics

3/3

Page 3 of 3

Problem #4 (30 points) Semiconductor p-n junctions

The junction between positively (p)-doped and negatively (n)-doped silicon is at the heart ofmodern semiconductor devices, including p- n diodes and transistors. We can model an abrupt

junction as a dielectric material ( = 11.9 0 for silicon) with four regions with charge density

( x).

0

00

0

0

0

0 for

for 0,( )

for 0 ,

0 for +

x x

x x x

x x

x x

In this expression, 0 is a constant charge density, and x0 is a length of the depletion region on the p-side (- x0< x