CHAPTER ONE: 1-1: For a cylindrical coordinate prove that p = Vy? + x2 1-2: Given a part of cylinder with 2 < p <3, 30° < Ø < 60° , 0
CHAPTER ONE: 1-1: For a cylindrical coordinate prove that p = Vy? + x2 1-2: Given a part of cylinder with 2 < p <3, 30° < Ø < 60° , 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![CHAPTER ONE:
1-1: For a cylindrical coordinate prove that p =
Vy2 + x2
1-2: Given a part of cylinder with 2 < p < 3, 30° < Ø < 60°, 0 <z <4, Find all
surface and volume.
1-3: Find the surface area of hemisphere that radius = 3.
1-4: For a spherical coordinate prove that r sin(0)
y2 + x2
1-5: Convert F =r cos(Ø) ar to Cartesian at point ( 4,90° , 60°)
1-6: Convert F =r cos( Ø) aR to Cartesian.
CHAPTER TWO:
2-1: Find the electric field intensity ( E) due to the following charges at point ( 2,3,4),
Given: Q
4 µC at origin
P = 4 µc/m at x = 1 and y = 0
Ps1
= -4 µc/m2 at y = 4
Ps1 = 6 µc/m2 at z = -3
2-2: A line charge at y-axis with P = 30 nc/m, Find the electric field intensity ( E) at
point (0,0,3) for:
%3D
a- -4 <y < 4
b- 0 <y <4
c- -00 <y < o
2-3: A line charge with P = 10 |x| nc/m at -3 Sx < 3, Find (E) at point ( 0,4,0)
2-4: A circular ring of radius ( a ) with uniform charge P c/m is placed on xy - plane
z = 0, Prove that
P. a.h
E
( 0,0,h)
2 ɛ, [ a? + h?]/2
2-5: Given Py:
= 6 ɛ, c/m3 find and draw electric field intensity (E) everywhere.
2-6: Find the stream line equation of E = = az
az at point ( 2,1,3)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05763628-f352-4f4a-9ae7-829c7b236811%2F4fa52797-7d07-49fd-af59-5db20ee238a9%2Ftrdzvtd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:CHAPTER ONE:
1-1: For a cylindrical coordinate prove that p =
Vy2 + x2
1-2: Given a part of cylinder with 2 < p < 3, 30° < Ø < 60°, 0 <z <4, Find all
surface and volume.
1-3: Find the surface area of hemisphere that radius = 3.
1-4: For a spherical coordinate prove that r sin(0)
y2 + x2
1-5: Convert F =r cos(Ø) ar to Cartesian at point ( 4,90° , 60°)
1-6: Convert F =r cos( Ø) aR to Cartesian.
CHAPTER TWO:
2-1: Find the electric field intensity ( E) due to the following charges at point ( 2,3,4),
Given: Q
4 µC at origin
P = 4 µc/m at x = 1 and y = 0
Ps1
= -4 µc/m2 at y = 4
Ps1 = 6 µc/m2 at z = -3
2-2: A line charge at y-axis with P = 30 nc/m, Find the electric field intensity ( E) at
point (0,0,3) for:
%3D
a- -4 <y < 4
b- 0 <y <4
c- -00 <y < o
2-3: A line charge with P = 10 |x| nc/m at -3 Sx < 3, Find (E) at point ( 0,4,0)
2-4: A circular ring of radius ( a ) with uniform charge P c/m is placed on xy - plane
z = 0, Prove that
P. a.h
E
( 0,0,h)
2 ɛ, [ a? + h?]/2
2-5: Given Py:
= 6 ɛ, c/m3 find and draw electric field intensity (E) everywhere.
2-6: Find the stream line equation of E = = az
az at point ( 2,1,3)
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