Electric Forces Homework: Calculate Two Point Charges Using Coulomb's Law

[dwn]

Homework Statement

Two point charges are 3 m apart and their combined charge is 20µC. If they
repel each other with a fore of 0.075 N, what are the two charges? Ans: 15 μC and 5μC


Homework Equations

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

(could someone mention in their response how we use the math text in our posts, so that I can make it more convenient for the reader)

The Attempt at a Solution

I'm really not so sure where to begin here, but I made a few attempts by manipulating both q₂ and q₂. I will post one of them below:

9*10⁹ (q₁+q₂)/3²=0.075N

 

[Doc Al]

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

Good.

(could someone mention in their response how we use the math text in our posts, so that I can make it more convenient for the reader)

Check out the FAQ, under "SITE INFO/Frequently Asked Questions" at the top of every page.

The Attempt at a Solution

I'm really not so sure where to begin here, but I made a few attempts by manipulating both q₂ and q₂. I will post one of them below:

9*10⁹ (q₁+q₂)/3²=0.075N

The one mistake you made was to use q₁+q₂ instead of q₁*q₂.

The second equation you'll need is q₁+q₂ = ??

 

[dwn]

I tried that in one of my attempts, but I don't see the "bridge" between the two equations.

If I solve Coulombs equation for q1*q2, I don't see where I'm supposed to plug in q1+q2 = 20 into the other equation...?

 

[Doc Al]

I tried that in one of my attempts, but I don't see the "bridge" between the two equations.

If I solve Coulombs equation for q1*q2, I don't see where I'm supposed to plug in q1+q2 = 20 into the other equation...?

You'll have two equations and two unknowns. Solve them simultaneously, using any method you like. (Such as substitution.)

 

[Nickie]

First of all, great job on attempting the problem and showing your work. It seems like you have the right equation, which is Coulomb's Law, and you are on the right track. To use math text in posts, you can use the LaTeX format by enclosing your equation or formula within two dollar signs ($$). For example, the equation you have written would look like this:

$$F=\frac{k(q_1q_2)}{r^2}$$

To solve the problem, you need to use the given information and the equation you have correctly identified. The distance between the two charges is given as 3m, so r=3m. The combined charge of the two charges is given as 20μC, so q1+q2=20μC. The force of repulsion is given as 0.075N, so F=0.075N. Now, plugging these values into the equation, we get:

$$0.075N=\frac{9*10^9(q_1*20μC)}{(3m)^2}$$

Simplifying this, we get:

$$0.075N=\frac{3*10^8(q_1)}{9}$$

Solving for q1, we get:

$$q_1=15μC$$

Since the total charge is 20μC, we can find q2 by subtracting q1 from 20μC, which gives us:

$$q_2=20μC-15μC=5μC$$

Therefore, the charges on the two point charges are 15μC and 5μC, as you have correctly stated in your original attempt.

In summary, to solve this problem, you need to correctly identify the relevant equation (Coulomb's Law), plug in the given values, and solve for the unknown charges. It's important to keep track of units and use proper algebraic manipulation to arrive at the correct answer. Great job on attempting the problem and showing your work! Keep up the good work.