Electromagnetism vectors question. Calculating electric flux of displacement vector

1. Jan 20, 2012

michael2812

Using cylindrical co-ordinates (r, theta, z), calculate the electric flux
phi=integral D . dS
when the displacement vector D is given by:
D=10ezcos(theta)/r2 . kr + z2sin(theta)/r2 . Kz and the surface S is part of a cylinder of radius a=0.3, defined by 0 is less than or equal to z which is less than or equal to 1 and 0 is less than equal to theta which is less than or equal to pi/4

I’ve put the equation in the cylindrical co-ordinates:

(10ezcos(theta)/r2, 0, z2sin(theta)/r2)

From there I’ve written out S as S(Sr, Stheta, Sz)

I know that the perpendicular lines define the surface. In this case Sz is perpendicular which means than Sr is the main component.
Then:

D . DS = DrdSr + DthetadStheta + DzdSz

But I don’t know where to go from here..... Any help?