Solution - California State University, Bakersfield3 QUESTION 2:(25 POINTS) Vector field E is...
Transcript of Solution - California State University, Bakersfield3 QUESTION 2:(25 POINTS) Vector field E is...
CALIFORNIA STATE UNIVERSITY, BAKERSFIELD (CSUB)
DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING & COMPUTER SCIENCE
ECE 3320: FIELDS AND WAVES
Homework 3
Solution
QUESTION 1:(25 POINTS)
For each of the following vector fields, determine ∇ · A analytically and then compare the result with your
expectations on the basis of the displayed pattern.
Answer:
1
2
3
QUESTION 2:(25 POINTS)
Vector field E is characterized by the following properties: (a) E points along R, (b) the magnitude of E is a
function of only the distance from the origin, (c) E vanishes at the origin, and (d) ∇ · E = 12, everywhere. Find
an expression for E that satisfies these properties.
Answer:
4
QUESTION 3:(25 POINTS)
A vector field D = rr3 exists in the region between two concentric cylindrical surfaces defined by r = 1 and
r = 2, with both cylinders extending between z = 0 and z = 5. Verify the divergence theorem by evaluating:
a)∮S D · ds
b)∫ν ∇ ·D dν
Answer:
5
QUESTION 4:(25 POINTS)
For the vector field E = xxy − y(x2 + 2y2), calculate
a)∮C E · dl around the triangular contour shown in the following figure.
b)∫S(∇×E) · ds over the area of the triangle.
Answer:
6