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

Given an equilateral triangle with sides 20-cm, with point charges at each point:

qat the top with a charge of +4.0_{1}uM,

qat the bottom right with a charge of -4.0_{2}uM, and

qat the bottom left with a charge of +4.0_{3}uM.

kis assumed to be exactly 9.00x10^{9}N-m^{2}/c^{2}

Question: What is the electric field at the center of the triangle?

2. Relevant equations

E = (kq)/r^{2}

3. The attempt at a solution

First and foremost, I employed a little geometry find the center of the triangle:

r = sqrt( (0.20-m)^{2}- (0.10-m)^{2}) / 2

r = 0.866-m, rounded to

r = 0.90-m

E_{1}= (9.00x10^{6}N-m^{2}/c^{2})(4.0x10^{-6}C) / (0.09-m)^{2}

E_{1}= 4.4x10^{6}N/C

The magnitudes of all three charges are equivalent, so:

E_{1}= E_{2}= E_{3}

So the x and y components would be:

E_{x}= (4.4x10^{6}N/C)cos30° + (4.4x10^{6}N/C)cos330°

E_{x}= 7.6 x 10^{6}N/C

E_{y}= (4.4x10^{6}N/C)sin270° + (4.4x10^{6}N/C)sin30° + (4.4x10^{6}N/C)sin330°

E_{y}= -4.4x10^{6}N/C

E = sqrt[ (7.6 x 10^{6}N/C)^{2}- (4.4x10^{6}N/C)^{2}]

E = 6.2 x 10^{6}N/C

So, my answer is 6.2 x 10^{6}N, but the book answer key shows 5.4 x 10^{6}N/C. That is quite a significant difference, but I can't seem to find where I'm making a mistake. It's driving me mad!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Electric Field at the Center of a Triangle

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