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matt222
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Homework Statement
A vector field h is described in cylindrical polar coordinates by ( h equation attached )
where i, j, and k are the unit vectors along the Cartesian axes and
(er) is the unit vector (x/r) i+(y/r) j
Calculate (1) by surface integral h through the closed surface bounded by the cylinders r=a and r=2a and the planes z=-a*pi/2 to +a*pi/2
and (2) by divergence theorem.
Homework Equations
The Attempt at a Solution
1- I draw the equation and I found it is like hollow tube cylinder with radius of r of the inner surface and 2r for the outer surface
2-I found there are 6 surfaces
a- S1 pointing into -z direction
b- S2 pointing into +z direction
c- S3 pointing into -Y direction
d- S4 pointing into -x direction
e- S5 surface of the outer tube r= 2a
f- S6 surface of the inner tube r=a
I solved the 6 surfaces and the outcome
S1=0
S2=sin(lamda*a*pi/2)*pi*a^2/4
S3=y/lamda*sin(a*pi*lmda/2)
S4=x/lamda*sin(a*pi*lmda/2)
S5= pi/2*lamda[2sin(a*pi*lmda/2)-2acos(a*pi*lmda/2)+2a]
S6=pi/2*lamda[sin(a*pi*lmda/2)-acos(a*pi*lmda/2)+a]
adding them all up and compared them with divergence which I got are not the same, could anyone find out what mistake I did
the divergence I got was
3a*pi/4lamda*sin(a*pi*lmda/2)+7a^2*pi/6*cos(a*pi*lmda/2)+3a*pi/4sin(a*pi*lmda/2)+
7a^2*pi/6
which is not the same with what I got