Coulombs law stuff I dont know what they are asking

AI Thread Summary
The discussion revolves around a problem involving three charged particles and the application of Coulomb's law to find the position of a third charge, q3, such that the forces exerted on it by the first two charges are equal. Participants clarify that the problem requires finding two possible positions for charge 3, not its value, which is given as q. The approach involves setting up equations for the forces between the charges and equating them to solve for the position of charge 3 in terms of the known variables. The confusion arises from the lack of specific distances, but the solution can be derived by expressing distances in terms of the variable d. Ultimately, the problem can be solved by applying Coulomb's law correctly and understanding the relationships between the charges.
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Two charged particles, with charges q_1=q and q_2=4q, are located a distance d apart on the x axis. A third charged particle, with charge q_3=q, is placed on the x-axis such that the magnitude of the force that charge 1 exerts on charge 3 is equal to the force that charge 2 exerts on charge 3.
Find the position of charge 3. Assume that all three charges are positive.

So charge 3 could be inbetween charge 1 and 2, or to the left of charge 1. The problem wants me to find "2 possible VALUES" of charge 3. How can i find a value when no values were given to me in the word problem. THey want the X_3,1, and X_3,2 in terms of Q, D, and K (coulomb constant).
 
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red ink said:
Find the position of charge 3. Assume that all three charges are positive.

Okay, so it sounds like the problem is asking for you to find a location for charge 3 on the x-axis such that the electric forces exerted on it by each of the other two charges are equal (in magnitude).

red ink said:
The problem wants me to find "2 possible VALUES" of charge 3.

No, the value of charge 3 is given, q3 = q. You must mean that the problem wants you to find two possible positions for charge 3.

red ink said:
How can i find a value when no values were given to me in the word problem.

You answered that question yourself right here:

red ink said:
THey want the X_3,1, and X_3,2 in terms of Q, D, and K (coulomb constant).

This problem is a fairly straightforward application of Coulomb's law, which allows you to calculate the electric force between two charges given the magnitude of the charges and the distance between them. It shouldn't be too hard considering you're only working in one dimension. For simplicity, why not put q1 at the origin and q2 a distance d to the right? If q3 is at some position x3, just write an expression for the force exerted by each of the other two charges on it according to Coulomb's law.

e.g

F_{\textrm{2 \,on \,3}} = k\frac{q_2 q_3}{d-x_3} = k\frac{4q^2}{d-x_3}

Can you write a similar expression for the force due to q1 on q3? If the required condition is that these two forces must be equal, equate the expressions! :smile: Can you solve for x3?
 
Thank you in advance for your reply...forgive me for my poor formating in my posts. This LaTeX Code stuff is kinda confusing!

So by equate the expressions, you mean Force 1 on 3 will look just like the expression you gave me for Force 2 on 3, with the only difference being the numerator is "q^2" instead of 4q^2 since Charge 3=q?
F_{\textrm{1 \,on \,3}} = k\frac{q_1 q_3}{d-x_3} = k\frac{q^2}{d-x_3}
to solve for x_3, set F_{\textrm{1 \,on \,3}} = F_{\textrm{2 \,on \,3}}. This should give me a quadratic equation with 2 real value solutions?
x_3,1, x_3,2 = these values?
 
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You've almost got it, except that the expression for F 1 on 3 due to Coulomb's law should have in the denominator the *distance between charge 1 and charge 3.* What is this distance?
 
thats what stumpped me...they gave no distance. Only the varible "d". I already failed it online, but i'd like to know what i should have put. I had no clue what they were asking for.
 
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