Hello, Here is the question Iam having trouble with. Two point particles,each ha

Question

Hello,

Here is the question Iam having trouble with.

Two point particles,each having a charge equal to q, sit on the base ofan equilateral triangle that has sides oflength L as shown in the figure below. A thirdpoint particle that has a charge equalto Q = 4q sits at the apex of the triangle.A fourth point particle that has charge q' is placedat the midpoint of the baseline making the electric field at thecenter of the triangle equal to zero. What is the valueof q' ? (The center is in the plane of the triangleand equidistant from all three vertices.)

When I triedsolving this question, I came up with q' = 3.75q, which seemedright but apparently that is not the correct answer. I triedusing a vector sum to determine the charges vertically from 4q toq' taking in to account both q's. Anyone have anyideas?

Explanation / Answer

L = length of side x = distance from side to center d = distance from vertex to center (x + d)2 + (L / 2)2 =L2 (L / 2)2 + x2 =d2   from geometry of triangle Solve and get d = 2 x or x = L / 12 = 3 L/ 6 So if Q1 is the unknown charge 4 q / (d + x)2 = Q1 / x2 4 q / (9 x2) = Q1 /x2 Q1 = 4 q / 9    negative, of course- the fields due to the charges on either side cancel 4 q / (9 x2) = Q1 /x2 Q1 = 4 q / 9    negative, of course- the fields due to the charges on either side cancel Q1 = 4 q / 9    negative, of course- the fields due to the charges on either side cancel

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