Second year uni, e&m, dialectrics question?

[coffeem]

Hi there. I managed to get in a car accident before all of my summer exams so now have to take them all in September. I have started revising and I have a question which I cannot do.

A thin, circular disk of dialectic of radius 'a' carries a uniform positive sheet charge density of 'x'(C/m^2) and is placed in the horizontal plane. Calculate the strength of the electric field at a distance 'b' above the centre of the disk (assume surrounded by vacuum). Determine the value of this field in the limit when b<<a and comment briefly on this result.

I would go to office hours for help with this, but I am 200 miles away from uni. Please can hint as to what I have to do to get the answer. I do not want a solution as I would like to play some part in working it out. thanks

 

[jix]

Rings are key.

Split the disk into infinitesimal rings. I assume you have a decent handle on calculus, so first derive the electric field at distance b from a ring of radius r and thickness dr. Like, take infinitesimal segments (on an infinitesimal ring!) and calculate the fiield, integrate to sum them up. After that, integrate the result from 0 to a (sum over the radii of the rings), and you'll get the total electirc field.

As for the b<<a thing, think of what the disk looks like from the point of view of the charge. This part is easy.

 

[LowlyPion]

This link might also prove useful:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesht.html#c1

 

[coffeem]

Thank you both so much. Once I got what I had to do the hardest part was a pretty trivial integral. No doubt I will be posting many more messages asking for help in the next few weeks.