# A Polarization Problem

1. Aug 24, 2006

### Saketh

I'm trying to teach myself polarization and dielectrics by doing problems, but it's not going as well as I'd hoped. Here's the first problem that I got stuck on:
A round dielectric disc of radius R is statically polarized so that it gains the uniform polarization P, with the vector P lying in the plane of the disc. Find the strength E of the electric field at the center of the disc if d << R. ​
I thought that since the disc is polarized along its plane, there would be a charge density $$\sigma$$ on one half of it, and a charge density of $$-\sigma$$ on the other half of it. I wasn't sure if $$\sigma = P$$, but I set them equal anyway. I also wasn't sure if $$\sigma$$ is uniform along each half-surface, but I did that anyway. Then I thought that a uniform polarization vector means that the whole surface is charged up unformly, which means no net electric field at the center.

I realize this is going to sound silly, but I have no idea how I'm supposed to solve this problem. Where am I supposed to start?

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: A Polarization Problem
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8944184184074402, "perplexity": 339.9430790351687}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218190134.25/warc/CC-MAIN-20170322212950-00169-ip-10-233-31-227.ec2.internal.warc.gz"}