Gravitational field owing to a uniform circular plate

[Dumbledore211]

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Homework Statement

Show that the gravitational field due to thin uniform circular plate of radius a at point distant R from center and on the axis passing through the center and perpendicular to the plane of the plate is given by E= -2πGρ[1-R/(a^2+R^2)^1/2]

Homework Equations

F= GMm/r^2
E=F/m

The Attempt at a Solution

I really don't have any proper approach as to how I should go about this problem. How am I going to get a negative sign in the field created by the plate making sure the field is on the vertical axis passing through the center? Would be very helpful if any of you could drop a hint as to how I should start this problem as I am at a total loss with this one.

 

[Nathanael]

I'm not really sure what your confusion is. Your goal is to find the force per mass on an object which lies on a line that is perpendicular to the circle and passes through the center of the circle. Call the distance to the center of the circle R and integrate the force from each differential piece of mass (remembering that force is a vector) in which ever way you think is easiest.