Search: To find out answers to a specific question, copy a representative sentence from the question and paste the sentence in the search form and search it. The results show the most related questions and yours may be in there. Feel free to share LeiAcademy.org with other teachers and students.  
To discourage spam, only registered users can ask questions.

Welcome to Physics Homework and Study Help, where you can ask questions and receive help on learning physics. We currently focus on helping questions in introductory level college physics and high school AP Physics courses.
To discourage spam, only registered users can ask questions.

Facebook Twitter Google

Welcome to Physics Homework Help Page on LeiAcademy.org

Feel free to ask a question and also answer questions others asked. Answering others' questions can in turn help one's own understanding and build a warm healthy community for learning. The followings list a few things that might be helpful for you to effectively obtain help on specific physics homework or practice problems.  

Search: To find out answers to a specific questions, copy a representative sentence from the question and paste the whole sentence in the search form and search it. The results will show the most related questions and yours may be in there

Browse: To find out what have been discussed, asked or answered, put in a few key words in the search form and search for related questions, answers, and or solutions. Or you can click the related tags or other tabs to find useful information there. 

You can also write professional-looking equations using Latex codes (see details here).

This site is hosted on LeiAcademy.org, which will continue to add new resources for learning. Feel free to share this with other teachers and students.  

Two fixed charges of 1.0uC and 3.0uC are 15cm apart. Where would you place a third charge...

0 votes
132 views

Two fixed charges of 1.0uC and 3.0uC are 15cm apart. Where would you place a
third charge so that no net electrostatic force acts on it?

The Us before the Cs represent micro. I know how to use coulombs law for 2 charges but here I am lost, please help.

asked Mar 5, 2014 in Intro College Physics by marcgab (120 points)

1 Answer

0 votes
We want to find the place were the net force on the third charge is zero. Essentially we are using Coulombs law twice (once with charges 1 and 3, and then once with charges 2 and 3) and ensuring that it is equal both times by carefully placing the third particleTo do so we may set up Newton's equation (The particles should be in a line so only one-dimension):

$$\Sigma F_3 = 0 = F_1 + F_2 = \frac{ k q_1 q_3}{ r_1^2} - \frac{k q_2 q_3}{r_2^2}$$

Here \(r_1\) is the distance between charge 1 and charge 3, and \(r_2\) is the distance between charge 2 and charge 3. We know that \(r_1 + r_2 = d \) according to the problem statement ( \( d= 15 cm \) ). The minus sign in front of the force from charge 2 signifies that it is acting in the opposite direction of charge 1.

Dividing out the common factors and a bit of algebra:

$$\frac{q_1}{r_1^2} = \frac{q_2}{(d - r_1)^2}$$

$$ q_1 (d^2 -2 d r_1 + r_1^2) = q_2 r_1^2$$

$$ (q_1 - q_2) r_1^2 - 2 q_1 d r_1 + q_1 d^2 = 0$$

Here we are left with a quadratic equation which can be solved using the quadratic formula leaving us with:

$$r_1 = 5.5 cm$$

Note that the quadratic equation will yield two answers...you need to choose which makes sense in this situation. In this case, only one is between 0 and 15 cm and that is your answer.
answered Mar 13, 2014 by jcf1559 (2,140 points)
web counter
...