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

In summary, the conversation discusses the use of Coulomb's equation (F=k(q1*q2)/r^2) to solve for the two charges of two point charges located 3m apart with a combined charge of 20µC that repel each other with a force of 0.075N. The conversation also mentions the use of math text in posts and directs readers to the FAQ for more information. The solution involves setting up two equations, one with q1 and q2 as variables and the other with q1+q2=20, and solving them simultaneously to find the two charges.
  • #1
dwn
165
2

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
 
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  • #2
dwn said:
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 = ??
 
  • #3
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...?
 
  • #4
dwn said:
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.)
 
  • #5


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.
 

What is Coulomb's Law?

Coulomb's Law is a fundamental law in physics that describes the electric force between two stationary charged particles. It states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

How do I calculate the electric force between two point charges using Coulomb's Law?

To calculate the electric force, you will need to know the charges of the two particles and the distance between them. Then, you can use the formula F = k * (q1 * q2) / r^2, where k is the Coulomb's constant, q1 and q2 are the charges of the particles, and r is the distance between them. Make sure to use consistent units for charge and distance.

What is the unit of electric force?

The unit of electric force is Newtons (N). This is the same unit used to measure other types of forces, such as gravitational force.

Can Coulomb's Law be applied to point charges with opposite signs?

Yes, Coulomb's Law can be applied to point charges with opposite signs. The force calculated using this law will be attractive if the charges have opposite signs, and repulsive if they have the same sign.

What happens to the electric force when the distance between two point charges is doubled?

According to Coulomb's Law, the electric force between two point charges is inversely proportional to the square of the distance between them. This means that if the distance between the two charges is doubled, the force will decrease by a factor of four. In other words, the force decreases as the distance increases.

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