Suppose Q 1 (0 .0,-3 .0m,0 .0)=4 .0 nC, Q 2 (0 .0,3 .0m,0 .0)=4 .0 nC, and Q 3 (4 .0 m,0 .0,0 .0)=1 .0 nC . (a) Find the total force acting on the charge Q 3 . (b) Repeat the problem after changing the charge of Q 2 to –4.0 nC. (c) Find the electric field intensity for parts (a) and (b).
Suppose Q 1 (0 .0,-3 .0m,0 .0)=4 .0 nC, Q 2 (0 .0,3 .0m,0 .0)=4 .0 nC, and Q 3 (4 .0 m,0 .0,0 .0)=1 .0 nC . (a) Find the total force acting on the charge Q 3 . (b) Repeat the problem after changing the charge of Q 2 to –4.0 nC. (c) Find the electric field intensity for parts (a) and (b).
Solution Summary: The author explains the total force that acts on charge Q_3 and its value.
Q
2
(0
.0,3
.0m,0
.0)=4
.0
nC,
and
Q
3
(4
.0 m,0
.0,0
.0)=1
.0
nC
. (a) Find the total force acting on the charge Q3. (b) Repeat the problem after changing the charge of Q2 to –4.0 nC. (c) Find the electric field intensity for parts (a) and (b).
Find Eigenvalues and Eigenvectors for the following matrices:
[10
4
A=0
2
0
3
1
1 -3
1. (20 pts) Plot the pulse and the FFT for a pulse with the following properties at x=0 and x=10
cm.
f=2 MHz
m=3
Ncyc=2, 6, 20
po 1 MPa (source pressure)
x=10 cm (propagates in a Newtonian fluid for 10 cm as a plane wave-not a sound beam)
a=0.5 dB/(MHz cm)
Consider 3 types of waves: sine, square, and sawtooth. (square and sawtooth only for grad
students)
Observe your plots and draw some conclusions. Discuss any possible issues you encounter.
2. (20 pts) We have the following 3 ultrasonic transducers:
a. Focused 1 MHz, 2.54 cm diameter, 5.08 cm focus
b. Focused 3 MHz, 2.54 cm diameter, 5.08 cm focus
c. Unfocused 0.1 MHz, 2.54 cm diameter
The transducers are operating in water (c=1486 m/s).
I. Plot the axial field for all transducers
II. Plot the focal transverse field for the focused transducers and the transverse field at the
Rayleigh distance (R_0) and at 2R_0 for the unfocused.
III. Assume source pressure of 0.1 MPa, and find the acoustic pressure in MPa at the location
(r=0, z=4.5…
Find the Q-points for the diodes in the circuit. Assume ideal diodes, and startwith the assumption that D is OFF, and D2 is ON for both circuits.
Chapter 2 Solutions
Fundamentals of Electromagnetics with Engineering Applications
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