Electric Field Question: Finding Zero Point Between Two Charges on Y-Axis

AI Thread Summary
Two point charges, q1 = -9 μC at y = 6.0 m and q2 = -8.0 μC at y = -4.0 m, are analyzed to find the point along the y-axis where the electric field is zero. The initial equations set up to find this point contained a typo, which was corrected to reflect the correct distances from the charges. The discussion highlights the need to simplify the equations correctly, particularly by taking square roots and ensuring positive values. A suggestion was made to multiply both sides of the equation by (r + 4) to solve for r, which helped overcome a mental block in the problem-solving process. The conversation emphasizes the importance of careful setup and algebraic manipulation in solving electric field problems.
thebigbluedeamon
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I need a little guidance in this problem...

Two point charges lie along the y-axis. A charge of q1=-9 mu*C is at y=6.0m, and a charge of q2=-8.0 mu*C is at y=-4.0 m. Locate the point (other than infinity) at which the total electric field is zero.

So,

I made the statement

E1y = -E2y

and

Ke (q1/(r-4)^2) = Ke (q2/(r+4)^2)
or
q1/(r-6)^2 = q2/(r+4)^2

But that makes it very hard to solve for r. Is that equation set up correctly? If so, what is the easiest way, algebraicly, to solve for r.
 
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thebigbluedeamon said:
Ke (q1/(r-4)^2) = Ke (q2/(r+4)^2)
or
q1/(r-6)^2 = q2/(r+4)^2

But that makes it very hard to solve for r. Is that equation set up correctly? If so, what is the easiest way, algebraicly, to solve for r.
I think you have a typo in the equation above. Take the square root of both sides and simplify.
 
e(ho0n3 said:
I think you have a typo in the equation above. Take the square root of both sides and simplify.

I did have a typo...It was supposed to be a 6 instead of a 4 in the first equation.

Let me try this and hopefully I can solve.
 
Okay...so I took the square root of both sides of the equation, but that doesn't seem to get me very far.

I end up with:

sqrt(q1/q2) = (r-6)/(r-4)

And frankly I don't know how to solve for r in this situation. I could use Maple or something, but it seems that this problem shouldn't require that. I think I might have got the initial set up wrong.
 
thebigbluedeamon said:
sqrt(q1/q2) = (r-6)/(r-4)
Two problems: (1) another typo, and (2) when you take square roots you better be sure your answer is positive.

Your equation should be: sqrt(q1/q2) = (6-r)/(r+4)
And frankly I don't know how to solve for r in this situation.
Start by multiplying both sides by (r+4). It's a simple linear equation.
 
Of course it is. I just had a mental block. I wouldn't have caught the "(6-r)" though. Thanks for your help.
 
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