Solving Charges: Coulomb's Law Puzzle

In summary: Capacitance is the measure of how much an object can store, and for two spheres, the capacitance would be the sum of the charges on each sphere.
  • #1
Saladsamurai
3,020
7
Stupid Charges!

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of .108 N when their center-to-center separation is 50 cm. The spheres are then connected by a thin conducting wire. When the wire is disconnected, the spheres repel each other with an electrostatic force of .036 N. Of the initial charges on the spheres, with a positive net charge, what was the (a) negative charge of one of them and (b) the positive charge of the other?

Well I know that I need to use Coulomb's Law since that is all we have studied. I know that I have one equation

[tex]F_{12}=\frac{k|q_1||q_2|}{r^2}[/tex]

[tex]\Rightarrow \frac{k|q_1||q_2|}{.5^2}=.108[/tex]

But I am having a hard time writing the second equation in terms of [itex]q_1[/itex] and [itex]q_2[/itex].

I know that [itex]q_1+q_2[/itex] is a positive number, that should help.

Any hints??

Thanks,
Casey
 
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  • #2
Would my second equation be [tex]\frac{k|\frac{q_1}{2}||\frac{q_2}{2}}{.5^2}=.036[/tex]

since the charge must distribute uniformly between the spheres? My prof gave me a hint that the second equation should be [tex]F=k*\frac{(q_1+q_2)^2}{4r^2}[/tex] But I have no idea where he got that?!
 
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  • #3
Saladsamurai said:
Would my second equation be [tex]\frac{k|\frac{q_1}{2}||\frac{q_2}{2}}{.5^2}=.036[/tex]

since the charge must distribute uniformly between the spheres?


When the spheres are connected, the potential of the two spheres become equal and the charge is divided according to that, not evenly as you are assuming. You have to use the formula for the capacitance of a sphere, and calculate the charge on each. The only thing that remains constant is the sum of the charges.
 
  • #4
Shooting star said:
When the spheres are connected, the potential of the two spheres become equal and the charge is divided according to that, not evenly as you are assuming. You have to use the formula for the capacitance of a sphere, and calculate the charge on each. The only thing that remains constant is the sum of the charges.

Thanks Shooting Star, but we have not learned anything about capacitance in the text yet; the chapter consists of ONLY Coulomb's Law. The charge should distribute evenly. There is an example problem that is somewhat similar in which say explain that since the spheres are identical, the charge will be uniform.

Basically, I can only use Coulomb's Law for this.

Can anyone see where my professor got the hint [tex]F=k*\frac{(q_1+q_2)^2}{4r^2}[/tex] from?
 
  • #5
Since the spheres are identical, the charge should distribute uniformly. While q1 and q2 are before the wire and q1' and q2' after, take the change in charge of q1 is equal to the change of charge of q2. Since they attract at first, take q1 to be negative and q2 to be positive. Since the net charge is positive initially, q1 + q2 is positive. And since charge is conserved, q1' + q2' = q1 + q2, which is positive on both sides. Since the charges repel afterward, with the net charge as positive, then both q1' and q2' should be positive.
 
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  • #6
Okay. And since the charges distribute evenly [itex]q_1'=q_2'=\frac{q_1+q_2}{2}[/itex] and that looks to me like it should do it. Charge is conserved, nice call. Thanks!
 
  • #7
Saladsamurai said:
Thanks Shooting Star, but we have not learned anything about capacitance in the text yet; the chapter consists of ONLY Coulomb's Law. The charge should distribute evenly. There is an example problem that is somewhat similar in which say explain that since the spheres are identical, the charge will be uniform.

Somehow, I had overlooked the word identical spheres, and that's why I went off on a different direction. Gear300 suggested the correct way, and you've got it.
 

Related to Solving Charges: Coulomb's Law Puzzle

1. What is Coulomb's Law and how does it relate to solving charges?

Coulomb's Law is a fundamental law of physics that describes the electrostatic force between two charged particles. It states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. This law is essential for solving charges as it provides a mathematical formula for calculating the force between two charges.

2. How do I determine the direction of the force between two charges using Coulomb's Law?

The direction of the force between two charges can be determined by the relative positions of the charges. If the charges are of opposite signs, the force will be attractive, drawing the charges towards each other. If the charges are of the same sign, the force will be repulsive, pushing the charges away from each other. Additionally, the force will always act along the line connecting the two charges.

3. Can Coulomb's Law be used to calculate the force between more than two charges?

Yes, Coulomb's Law can be extended to calculate the force between multiple charges. The total force on a single charge due to multiple charges can be found by summing the individual forces between that charge and each of the other charges. However, this calculation can become more complex when dealing with multiple charges.

4. How does distance affect the force between two charges according to Coulomb's Law?

According to Coulomb's Law, the force between two charges is inversely proportional to the square of the distance between them. This means that as the distance between two charges increases, the force between them decreases. Conversely, as the distance decreases, the force increases.

5. Are there any limitations to Coulomb's Law in solving charges?

While Coulomb's Law is a powerful tool for calculating the force between charges, it does have some limitations. It assumes that the charges are stationary and that the charges are point charges with no dimensions. In reality, charges can be in motion and have physical dimensions that can affect the force between them. Additionally, Coulomb's Law only applies to electrostatic forces and does not take into account any other types of interactions between charges.

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