in this electrostatics question i have a disk with a radius of R, and i have a charge q placed at a distance of R/2 perpendicular to the disk from its centre. i am asked to find the flux through the disk

WHAT I DID:-- here are my calculations and i diagram

http://picasaweb.google.com/devanlevin/DropBox?authkey=Gv1sRgCL_4l4PpvP_YsQE#5312348851145303922 [Broken]

i take an imaginary "container" as my gauss surface, which is a half sphere "bowl" on one side and the "lid" is my disk. now the flux in through the bowl is my flux out through the lid since there is no charge inside my container,

i took a spherical surface with a radius of sqrt(5/4)R which is flat on one side(the disk -green in my diagram)since there is no internal charge, all the ingoing flux, (through the disk) is equal to the outgoing flux( through the spherical part)

now the area of the shere is 2pi*r*h which comes to [(5-sqrt5)/2]pi*R^2

flux=E*A=(Kq/r^2)*(2pi*r*h)

flux=0.27(q/epsilon) ===>which is the fluc throught the bowl part, so the flux throught the disk is

flux=(-0.27(q/epsilon)) right??

but the correct answer in my textbook is exactly half of this??

can anyone see where i have gone wrong?

WHAT I DID:-- here are my calculations and i diagram

http://picasaweb.google.com/devanlevin/DropBox?authkey=Gv1sRgCL_4l4PpvP_YsQE#5312348851145303922 [Broken]

i take an imaginary "container" as my gauss surface, which is a half sphere "bowl" on one side and the "lid" is my disk. now the flux in through the bowl is my flux out through the lid since there is no charge inside my container,

i took a spherical surface with a radius of sqrt(5/4)R which is flat on one side(the disk -green in my diagram)since there is no internal charge, all the ingoing flux, (through the disk) is equal to the outgoing flux( through the spherical part)

now the area of the shere is 2pi*r*h which comes to [(5-sqrt5)/2]pi*R^2

flux=E*A=(Kq/r^2)*(2pi*r*h)

flux=0.27(q/epsilon) ===>which is the fluc throught the bowl part, so the flux throught the disk is

flux=(-0.27(q/epsilon)) right??

but the correct answer in my textbook is exactly half of this??

can anyone see where i have gone wrong?

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