Physics Help Forum Slight misunderstanding with a coulombs law question

 Electricity and Magnetism Electricity and Magnetism Physics Help Forum

 Jul 21st 2018, 12:43 PM #1 Junior Member   Join Date: Jul 2018 Posts: 1 Slight misunderstanding with a coulombs law question Hi there, The question reads as: Two point charges $\displaystyle +q_{1}$ and $\displaystyle +q_{2}$ are positioned at (-a,0) and (+a,0). If $\displaystyle +q_{1}=+q$ and $\displaystyle +q_{2}=+3q$, determine the position on the x-axis where the electric fields $\displaystyle \underline{E_{1}}$ and $\displaystyle \underline{E_{2}}$ are equal and opposite. The way I tackled this was I made a sketch and solved for x. I got $\displaystyle E_{1}=\frac{q}{4\pi\epsilon(a-x)^2}$ and $\displaystyle E_{2}=\frac{3q}{4\pi\epsilon(a+x)^2}$ and then made them equal and solved for x using the quadratic equation however the solution I was given shows the answer as needing $\displaystyle E_{1}=\frac{q}{4\pi\epsilon(a+x)^2}$ and $\displaystyle E_{2}=\frac{3q}{4\pi\epsilon(a-x)^2}$ clearly i've gotten messed up with the value of distance but I can't seem to see why. many thanks Seb
 Jul 22nd 2018, 06:38 AM #2 Senior Member   Join Date: Apr 2015 Location: Somerset, England Posts: 995 Hello and welcome. Going about this by coordinate geometry is the hard way , although it would eventually work. You have two charges q and 3d a distance 2a apart. The only place the field vectors directly oppose is on a line between the two centres of charge as in my diagram. You seek the point where theyse vectors are equal and opposite. Call the distance from q d1 and the distance from 3q, d2 Then you can calculate the Field or Force vectors at this point. You don't need to bother with the constants ans they are they same and will cancel. You only need the ratio of d1/d2 Once you have found this you can apply this ratio to the total separation distance = (d1 + d2) = 2a. Sorry my scribbling is in the brainstorming phase but I have no time now to pretty it up. Attached Thumbnails
Jul 22nd 2018, 08:19 AM   #3
Physics Team

Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,570
 Originally Posted by unsedrent Hi there, The question reads as: Two point charges $\displaystyle +q_{1}$ and $\displaystyle +q_{2}$ are positioned at (-a,0) and (+a,0). If $\displaystyle +q_{1}=+q$ and $\displaystyle +q_{2}=+3q$, determine the position on the x-axis where the electric fields $\displaystyle \underline{E_{1}}$ and $\displaystyle \underline{E_{2}}$ are equal and opposite. The way I tackled this was I made a sketch and solved for x. I got $\displaystyle E_{1}=\frac{q}{4\pi\epsilon(a-x)^2}$ and $\displaystyle E_{2}=\frac{3q}{4\pi\epsilon(a+x)^2}$ and then made them equal and solved for x using the quadratic equation however the solution I was given shows the answer as needing $\displaystyle E_{1}=\frac{q}{4\pi\epsilon(a+x)^2}$ and $\displaystyle E_{2}=\frac{3q}{4\pi\epsilon(a-x)^2}$ clearly i've gotten messed up with the value of distance but I can't seem to see why. many thanks Seb
One problem is that you set them equal to each other when they are opposite. They are only equal in magnitude. To correct for this include a negative sign when you set them equal to each other. I.e. instead of E1 = E2 write E1 = -E2. See how that works.

Jul 22nd 2018, 09:04 AM   #4
Senior Member

Join Date: Apr 2015
Location: Somerset, England
Posts: 995
 See how that works.
Yes that would make the purely algebraic method work.

 Tags coulombs, law, misunderstanding, question, slight

 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post George321 General Physics 4 Feb 21st 2010 11:17 AM kaleb Electricity and Magnetism 1 Jan 1st 2010 10:53 PM darajava Advanced Electricity and Magnetism 2 May 29th 2009 11:14 AM