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The flux of F across S is TU 2п с 1/6 F [³6² -(a sin(p) cos(0)i + a sin(p) sin(0)j + a cos(p) k) a³ • (a² sin²(p) cos(0)i + a² ) ₁ + a² ( [] F. ds = = с Jo TU 2π 2π - L™ 1² C a³(sin³(y) + sin(y) cos²(y)) de do sin(p) de do Thus, the flux does not depend on the radius a. k) de do

The flux of F across S is TU 2п с 1/6 F [³6² -(a sin(p) cos(0)i + a sin(p) sin(0)j + a cos(p) k) a³ • (a² sin²(p) cos(0)i + a² ) ₁ + a² ( [] F. ds = = с Jo TU 2π 2π - L™ 1² C a³(sin³(y) + sin(y) cos²(y)) de do sin(p) de do Thus, the flux does not depend on the radius a. k) de do

Advanced Engineering Mathematics
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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Question
The flux of F across S is
 
 
S
F · dS		  = 
?
 
0
2?
 
0
c
a3
 (a sin(?) cos(?) i + a sin(?) sin(?) j + a cos(?) k)
                  · (a2 sin2(?) cos(?) i + a2 
 
 
 
 
 
 
 
 j + a2 
 
 
 
 
 
 
 
  k) d? d?
 
   = 
c
a3
 
?
 
0
2?
 
0
a3(sin3(?) + sin(?) cos2(?)) d? d?
 
   =  c
?
 
0
2?
 
0
sin(?) d? d?
 
   = 
 
 
 
 .
Thus, the flux does not depend on the radius a.
The flux of F across S is *2π C 16₁ F. ds = TU с -(a sin(y) cos(0)i + a sin(y) sin(0)j + a cos(p) k) )j + a² ( • (a² sin²(y) cos(0)i + a² ="²a³(sin³ (p) + sin(4) cos²(4)) de de Jo π *2π - ST 6² - C sin (4) de do Thus, the flux does not depend on the radius a. k) de do
Transcribed Image Text:The flux of F across S is *2π C 16₁ F. ds = TU с -(a sin(y) cos(0)i + a sin(y) sin(0)j + a cos(p) k) )j + a² ( • (a² sin²(y) cos(0)i + a² ="²a³(sin³ (p) + sin(4) cos²(4)) de de Jo π *2π - ST 6² - C sin (4) de do Thus, the flux does not depend on the radius a. k) de do
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