Methods of Images
I’ve had a very busy day today including giving a lecture on Electrostatics and the Method of Images and, in an unrelated lunch-hour activity, filing my tax return (and paying the requisite bill). The latter was the most emotionally draining.
With no time for a proper post, I thought I’d give some examples of the images produced by yesterday’s graduands, including some who used a particular approach called the Method of Selfies. Unfortunately some of these are spoiled by having a strange bearded person in the background.
But first you might like to try the following example using the actual Method of Images:
Given two parallel, grounded, infinite conducting planes a distance a apart, we place a charge +q between the plates, a distance x from one of them. What is the force on the charge?
This is, in fact, from Griffiths, David J. (2007) Introduction to Electrodynamics, 3rd Edition; Prentice Hall – Problem 3.35.
Solutions via the comments box as usual, please.
And now here are some of the official pictures from yesterday
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January 30, 2014 at 10:15 am
That problem goes a long way further back than 2007; as I recall it was in Pippard’s book of problems from 40 years ago and he made no claim to originality. I also recall that the infinite sum given by the method of images doesn’t converge if you do it for the potential and then differentiate to find the force; you have to sum the forces themselves from the images, which does converge.
January 30, 2014 at 11:14 am
I just checked and this problem came up in my 1B Mathematics Notes (course delivered by JN Stewart) under “Method of Images” along with a comment saying “best tackled by other methods…”
January 30, 2014 at 11:27 am
Shurely JM Stewart?
January 30, 2014 at 11:31 am
Ooops. Correct.
February 22, 2014 at 3:31 pm
[…] at the Dome, in Brighton, last month. I blogged about this here and there are also some pictures here. My stint commences at about 1:35:30 and finishes about 1:48:00 so there’s not too much of […]
May 23, 2016 at 8:37 pm
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