Solving Electric Field Zero: 0.20m Charges

AI Thread Summary
Two charges, +1.5x10^-6C and +3.0x10^-6C, are positioned 0.20m apart, and the goal is to find the point where the electric field is zero. The calculations involve setting the electric field strengths from both charges equal to each other, leading to the equation 1.5(0.2-x)^2 = 3.0(x^2). The user identifies a discrepancy in their results, obtaining -0.48 and 0.08, while the textbook states the answer should be 0.12m. They suspect an error in their calculations, particularly in the transition from the equation to the quadratic form. Clarification is sought on which specific line contains the mistake to resolve the issue.
jalen
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Homework Statement



+1.5x10^-6C, +3.0x10^-6C, 0.20m

Homework Equations



Two charges of +1.5x10^-6C and +3.0x10^-6C are 0.20m apart. Where is the electric field between them equal to zero?

The Attempt at a Solution



= (9.0x10^9)(1.5x10^-6C) + (9.0x10^9)(3.0x10^-6C)
x^2 (0.2-x)^2
1.5(0.2-x)^2=3.0(x^2)
(0.2-x)^2=2(x^2)
0.4-0.2x-0.2x+x^2=2x^2
-x^2-0.4+0.04=0

The answers you'll get are -0.48 and 0.08. The answer in the text is 1.2x10^-1m and you can get it if it's 0.06 instead of 0.04. I looked over my work but I can't find where I went wrong. =(
 
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The electric field strength due to Q1(at distance x from Q1)=The electric field strength due to Q2(at the distance of x from Q2)
 
Sorry, I don't really understand what you're trying to say. Can someone please tell me which line is incorrect so I can take a closer look and figure it out again.
 
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