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 Advanced Electricity and Magnetism Advanced Electricity and Magnetism Physics Help Forum May 9th 2016, 05:54 AM #1 Member   Join Date: Mar 2016 Location: Manchester Posts: 37 Use of equations in electromagnetism question I am having some trouble as to where the following equations came from when working out the following problems. Problem1: A electron is held 5 nm above a conducting metal surface. Use the method of images to calculate the induced surface charge density immediately below the electron on the surface of the plate. Equation used: sigma = -aQ/(2*pi(x^2+y^2+a^2)^3/2) I can do the problem and I understand the solution but I just don't know where the equation came from. Problem2: A electron is held 5 nm above a conducting metal surface. Use the method of images to calculate the force between the charge and the plate. Is the force attractive or repulsive? Equation used: F = -Q^2/(16*pi*e0*a^2) My question here is where did the 16pi come from? I though it was 4pi. Any help at all would be greatly appreciated   May 10th 2016, 12:01 PM #2 Physics Team   Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,336 The first equation comes from a calculation of the potential V as a function of position z, and then taking the derivative of epsilon_0 V(z) with respect to z and setting z=0. Here's a description of that: https://en.wikipedia.org/wiki/Method_of_image_charges As for the second equation - you're right that the equation for force has a factor of 4, but here the distance between the two particles is 2a, so that distance squared becomes 4 a^2. Hence the equation ends up with a factor of 16. Last edited by ChipB; May 10th 2016 at 12:20 PM.   May 10th 2016, 12:13 PM #3 Member   Join Date: Mar 2016 Location: Manchester Posts: 37 As always Chip, you've been awesome. Thank you so much for your help.  Tags electromagnetism, equations, question Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post Clyner82 Advanced Electricity and Magnetism 7 May 30th 2016 10:37 AM muon321 Theoretical Physics 11 Oct 7th 2013 04:45 PM tsang Advanced Electricity and Magnetism 1 Sep 14th 2010 02:55 PM physicsforumhelp Electricity and Magnetism 1 Oct 25th 2009 01:27 AM noor Electricity and Magnetism 3 May 3rd 2008 10:51 PM