Physics-electric charge(coulomb's law)

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To find the position where a third charge does not experience any force between two charges of 1.67 µC and -0.6 µC, the net forces from both charges must balance, leading to the equation F_1 + F_2 = 0. The initial setup was incorrect as it equated the forces without considering their opposing directions. The correct approach involves setting F_1 equal to -F_2, resulting in a solvable quadratic equation. The discussion emphasizes the importance of clear communication in problem-solving, particularly when sharing calculations. The corrected equation should yield a valid solution for the position of the third charge.
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The question is this:
Calculate the position on the line joining 2 charges 1.67 uC and -0.6uC situated 0.4m apart where a third charge q does not experience any force?

uC=microcoulomb
 

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The reason it comes out as a quadratic equation because there are two places that satisfy the problem
(You can place it at a certain distance to the left of the charges, or a certain distance to the right of the charges.)

The reason your quadratic was imaginary is because you set up the initial equation wrong.

You want F_1+F_2=0 and therefore F_1=-F_2 (Whereas you wrote "F_1=F_2" without the negative sign)



P.S.
In the future, it would be very helpful if you typed out your thoughts in the thread. The reason is that it can sometimes be difficult to read off of a picture. (And I almost didn't even notice that there were words in your picture!) Thank you :)
 
It did not give any solution
 
Let the point at which q_{3} does not experience any force be x.(Let this x be measured from q_{1})
Not distance of that specific point from q_{2}=(0.4-x)
Since net force on q_{3 } is zero so

kq_{1}q_{3}/x^{2}=-kq_{2}q_{3}/(0.4-x)^{2}
Put the values and get the answer.
 
josejayant13 said:
It did not give any solution

It does give a solution. Please re-check your calculations, what equation do you get after applying the correction Nathanael suggested?
 
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