Download hw2 - UCF EECS

Department of Electrical Engineering and Computer Science
EEL 3470 Electromagnetic Fields
Homework Set No. 2
Please turn in your answers, MatLab files and results.
Each group should turn in ONLY one set of homework.
Print this page and write your answers. After that, attach your MatLab files and results.
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Problem 1. In free space, the following charges appear:
(1) A 3 C point charge and a -4 C point charge are located at [-1 2 4] and [6 2
-3], respectively.
(2) An infinitely long uniform line charge with charge density 3 C/m is
distributed along [1 -2 1] direction and passing a point [3 4 6].
(3) An infinite charged sheet (uniform -4 C/m2) passing point [-2 1 3] with
normal direction point to [1 -2 7].
Find the electric field at point [3 -4 2] and [-2 9 0].
Answer:
Problem 2. Two charges of equal magnitude Q = 2(4 πε 0 ) C but with the opposite sign are
located at the points (1, 2) and at (5, 2) respectively on xoy plane. Find the
electric field E on the line that would correspond to x = 3 on xoy plane by
plotting E x , E y and Ez versus y in the region 4  y  8 .
Answer:
Problem 3. Assume that a total amount of charge equal to Q is distributed uniformly on
the circular ring defined by a    b . Find an analytical expression for the
electric field along the z axis. Plot the electric field distribution along z axis
( 5 m  z  5 m ) for a  1 m, b  2 m and Q = 2 nC.
y
a
x
b
Answer:
Problem 4. A line charge is distributed uniformly along a straight line from A(3,2,1) to
B(1,2,6). The total charge of this line is 3 nC (nano Coulomb). Find electric
field at point P(3,4,5). Note: the equation of the line from A to B can be
described by:
𝑥 − 𝑥𝐴
𝑦 − 𝑦𝐴
𝑧 − 𝑧𝐴
𝑙
=
=
=
𝑥𝐵 − 𝑥𝐴 𝑦𝐵 − 𝑦𝐴 𝑧𝐵 − 𝑧𝐴 𝐿
where L is the total length of the line and l is the distance along the line from
point A.
Answer:
Problem 5. A sheet charge plate is on yoz plane. The charge density is given by
(1  y 2 )(1  z 2 ) for  1  y  1,  1  z  1
0
elsewhere

Find: (1) total charge of the plate;
(2) electric field at (2, 3, -4).
s  
Problem 6. (1) Charge is distributed nonuniformly within a sphere of radius a as
v  0 r / a . Using Gauss’s law, calculate the electric field in the regions
r  a and r  a . Accurately sketch the electric field and label the axes ;
(Let a = 1, 𝜌0 = 1nC/m3, plot 𝐸𝑟 versus r from 0 to 5a).
(2) A charge of +Q is distributed uniformly in the central region 0    a
and –Q is distributed uniformly in the external region b    c of a
coaxial cable. Find the electric field in all regions of the coaxial cable and
sketch the results; (Q is total charge per unit length in z. Let a=1, b=3a,
c=4a, and Q = 1nC/m, plot 𝐸𝜌 versus 𝜌 from 0 to c).
c
a
b
(3) Charges are placed on the concentric hollow spheres. The values are:
Q(r  a)  2C ; Q(r  b)  4C where a  b  c . Find and sketch the
electric field in all regions r  0 . (Let a=1, b=2a, c=4a, plot 𝐸𝑟 versus 𝑟
from 0 to 10a).
c
a
b
Answer: (1)
(2)
(3)
Problem 7. The electric displacement D given in polar system by
𝐃 = 3𝜌2 𝐚𝛒 + 4cos⁡(𝜙)𝐚𝛟 − 3𝜌𝑧sin(𝜙)𝐚𝐳
Find total charge within spherical volume defined by:
2 ≤ 𝑟 ≤ 5,
15𝑜 ≤ 𝜃 ≤ 60𝑜 ,
30𝑜 ≤ 𝜙 ≤ 90𝑜
Note: based on Gauss’s law, the problem can be solved by either
(1) Evaluate the closed form integral ∯𝑆 𝐃 ∙ 𝐝𝐬 over the closed region.
(2) Calculate using ∭𝑉 (∇ ∙ 𝐃)𝑑𝑉.
Answer: (1)
(2)