Plum pudding model: Difference between revisions

Revision as of 12:46, 30 October 2024

Revision as of 18:18, 30 October 2024

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[[File:LbR relationship.svg|right|thumb]]

Since Thomson calculated the deflection would be very small, he treats ''L'' as a straight line. Therefore <math>L = 2\sqrt{R^2 - b^2}</math> where ''b'' is the distance of this [[chord (geometry)|chord]] from the centre. <math>\sqrt{L} = \sqrt{2\sqrt{R^2 - b^2}}</math>. The mean of <math>\sqrt{L}</math> is given by the integral

<math display="block">\frac{1}{\pi R^2} \int_0^R \sqrt{2 \sqrt{R^2 - b^2}} \cdot 2\pi b \cdot \mathrm{d}b = \frac{4}{5} \sqrt{2R}</math>