Second year uni, e&m, dialectrics question?

1. Jun 28, 2009

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

2. Jun 28, 2009

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.

3. Jun 28, 2009

LowlyPion

4. Jun 28, 2009

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.