Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 2, Problem 2.13P
A uniform volume charge density of 0.2 μC/m3 is present though out the spherical shell extending from r = 3 cm to r = 5 cm If pv=0 elseswhere, find (a) the total charge present through how the shell. and (b) if half the total charge is located in the region 3 cm
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The question was to obtain the Fourier series for the periodic function f(x)= -2 when -π
Consider the homogeneous RLC circuit (no voltage source) shown in the diagram below. Before
the switch is closed, the capacitor has an initial charge go and the circuit has an initial current go.
R
w
i(t)
q(t)
C
н
After the switches closes, current flows through the circuit and the capacitor begins to discharge.
The equation that describes the total voltage in the loop comes from Kirchoff's voltage law:
di(t)
L
+ Ri(t) + (t) = 0,
dt
(1)
where i(t) and q(t) are the current and capacitor charge as a function of time, L is the inductance,
R is the resistance, and C is the capacitance. Using the fact that the current equals the rate of
change of the capacitor charge, and dividing by L, we can write the following homogeneous (no
input source) differential equation for the charge on the capacitor:
ä(t)+2ag(t)+wg(t) = 0,
(2)
where
R
a
2L
and w₁ = C
LC
The solution to this second order linear differential equation can be written as:
where
81=
q(t) = Ae³¹- Bel
82 =
(3)
(4)
(5)
2.
1.
A. Simplify the models in the following block diagrams to open loop models (Y/R = G).
U(s) o
G₁
ROS
G₂
1-GG
G4
X₁
Σ
az
51-
515
G6
G₂
5
G₂
M
b₁
b₂
Σ
o Y(s)
X₁
by
Chapter 2 Solutions
Engineering Electromagnetics
Ch. 2 - Three point charges of equal magnitude q, that...Ch. 2 - Point charges of 1nC and -2 nC are located...Ch. 2 - Point charges of 50 nC each are located at...Ch. 2 - Eight identical point charges of Q C each are...Ch. 2 - A point charge of 3 nC is located at the point...Ch. 2 - Two point charges of equal magnitude q are...Ch. 2 - Point charges of equal magnitude but of opposite...Ch. 2 - A crude device for measuring charge consists of...Ch. 2 - A 100-nCpoint charges is located at A(-1,1,3)in...Ch. 2 - A configuration of point charges consists of a...
Ch. 2 - A charge Q0 located at the origin in free product...Ch. 2 - Electrons are in random in a fixed region in...Ch. 2 - A uniform volume charge density of 0.2 μC/m3 is...Ch. 2 - The electron beam in a certain cathode ray tube...Ch. 2 - A spherical volume having a 2-/μm radius contains...Ch. 2 - Within a region of free space, charge density...Ch. 2 - A length d of the charge lies on the Z-axis infree...Ch. 2 - (a) Find E in the plane z=0 that is produced by a...Ch. 2 - A line having charge density p0|C|C/m and of...Ch. 2 - A line charge of uniform charge density p0 C/m and...Ch. 2 - A charged filament forms a circle of radius a in...Ch. 2 - Prob. 2.22PCh. 2 - A disk of radius a in the xy plane carries surface...Ch. 2 - (a) Find the electric field on the z-axis produced...Ch. 2 - A disk of radius a in the xy plane carries surface...Ch. 2 - (a) Find the electric intensity on the z- axis...Ch. 2 - Given the electric field E=(4x2y)ax(2x+4y)ay, find...Ch. 2 - An electric dipole (introduced in Problem 2.7, and...Ch. 2 - If E=20e5y(cos5xaxsin5xay) ,find (a)...Ch. 2 - For fields that do not vary with z in cylindrical...
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