Coulomb's Law and Net Force

[Nghi]

Homework Statement

Two point charges lie on the x-axis. A charge of +7.7 uC is at the origin, and a charge of -4.4 uC is at x = 10.0 cm. At what position x would a third charge q3 be in equilibrium?

Homework Equations

F = k(q1)(q2)/r^2

The Attempt at a Solution

This was how I set up my diagram, and then I set F13 = F23.

F13 = k(q1)(q3)/x^2
F23 = k(q2)(q3)/(0.1-x)^2

k and q3 cancels out, so it becomes

q1/x^2 = q2/(0.1-x)^2
(7.7e-6)/(0.1^2) = (4.4e-6)/(0.1-x)^2

I got a final answer of 0.0244 m for x, or 2.44 cm. But it's not the right answer. What am I doing wrong? x__x

 

[anathema]

Thank you for your question. It seems like you have set up the problem correctly and have used the correct equation to solve for the equilibrium position of the third charge. However, there may be a small error in your calculation that is leading to the incorrect answer.

Firstly, please make sure that you are using the correct values for the charges. In the problem statement, the charges are given in microcoulombs (uC), but in your calculation, you have used the values in coulombs (C). Make sure to convert the charges to the correct unit before plugging them into the equation.

Secondly, when you cancel out the k and q3 terms, you should be left with:

q1/x^2 = q2/(0.1-x)^2

However, in your calculation, you have an extra 0.1^2 term on the left side of the equation, which may be leading to the incorrect answer. Please double check your calculations and make sure that you have not made any small errors in algebra.

I hope this helps. Let me know if you have any further questions.

 

[Moetasim]

Your approach seems correct, but it's possible that you made a calculation error. Make sure you are using the correct units for all variables (uC for charge and m for distance). Also, double check your algebraic steps to make sure you didn't make any mistakes. If you are still having trouble, try plugging in the given values for q1 and q2 and solving for x to see if you get the correct answer. It's also helpful to include units in your final answer to make sure it is the correct magnitude. Additionally, make sure you are using the correct value for the constant k, which is 8.99 x 10^9 Nm^2/C^2.