(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm having a lot of trouble solving for part b as I am unable to correctly apply the binomial theorem to this approximation. The problem is shown below:

Three point charges are distributed: a positive charge +2Q in the center, and a pair of negative charges -Q, a distanceato its left and right.

You want to find the electric fieldEat point P, a distancerto the right of the positive charge.

a) Write an exact expression for the x-component of E at point P (in terms ofQ,r,a, etc.

b) Using the binomial theorem, write a simpler approximation to the expression you gave in part b, which is valid when r>>a

2. Relevant equations

Binomial theorem: (1+x)^n=1+nx+n(n-1)x^2/2!+...

3. The attempt at a solution

a) I added the vector sum of all forces and got 1/(4pi epsilon knot)(-Q/(r+a)^2+(2Q)/r^2+(Q)/(r-a)^2

b) The professor gave out the answer for this part which is 6kQa^2/r^4, but we need to show how we got this. I go as far as KQ(2-(a-2a/r)-(1+2a/r))r^2, but I don't know how to proceed further. I wish I knew how to type out the work more neatly so you can see clearly. I would greatly appreciate any feedback.

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# Homework Help: Binomial Theorem and Electric Field question

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