Two nonconducting spheres problem

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In summary, two nonconducting spheres with a total charge of 13.4 μC are placed 0.362 m apart and experience a force of repulsion of 2.777 N. Using Coulomb's law, the equation F = K(q1)(q2)/r^2 and the equation q1 + q2 = 13.4x10^-6C, the value of the greater charge is found to be either 4.60x10^-6 C or 8.80x10^-6 C. However, these values do not match the correct answer. Further analysis is needed to identify where the error occurred.
  • #1
n77ler
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Homework Statement



Two nonconducting spheres have a total charge of 13.4 μC. When placed 0.362 m apart. the force of repulsion is 2.777 N. What is the value of the greater charge (Give your answer in coulombs)?

Homework Equations





The Attempt at a Solution

 
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  • #2
Hint: Coulomb's law.
 
  • #3
I tried this equation below because I just put in the total charge for Q and got the wrong answer. I don't understand how I get answers for two different charge swhen I work through it.
E= k (q1+q2) / r^2
 
  • #4
well first equation is F = K(q1)(q2)/r^2 and second equation is q1q2=13.4 μC
2 equations 2 unknowns.
 
  • #5
tongpu said:
well first equation is F = K(q1)(q2)/r^2 and second equation is q1q2=13.4 μC
2 equations 2 unknowns.
You are correct, but that second equation has a typo: it should be q1 + q2 = 13.4 μC
 
  • #6
F=kq1q2 / r^2 q1 + q2 = 13.4x10^-6C
2.777= (8.99x10^9)q1q2 /(0.362)^2
q1q2=4.05x10^-11
q1=(4.05x10^-11)/ q2

(4.05x10^-11)/q2 + q2 = 13.4x10^-6C
(4.05x10^-11)/ q2 + (q2^2)/q2 = 13.4x10^-6C
(4.05x10^-11) + (q2^2) = (13.4x10^-6C)q2
quadratic, when solved q2=4.60x10^-6, q2= 8.80x10^-6

Both of these numbers when added up will equal the total charge and when I sub them into the equation q1=(4.05x10^-11)/q2 I get the same thing. However this is not the correct answer, could someone point out where I went wrong?
 
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Related to Two nonconducting spheres problem

What is the "Two nonconducting spheres problem"?

The "Two nonconducting spheres problem" is a classic physics problem that involves two identical spheres, one with a positive charge and one with a negative charge, and asks for the electric field and potential at various points around the spheres.

What are the key concepts involved in solving the Two nonconducting spheres problem?

The key concepts involved in solving the Two nonconducting spheres problem include Coulomb's Law, which describes the force between two charged particles, as well as the principles of electric potential and electric field, which describe the behavior of charged particles in an electric field.

How do you approach solving the Two nonconducting spheres problem?

To solve the Two nonconducting spheres problem, you can use the principles of symmetry to simplify the problem and break it down into smaller, more manageable parts. You can also use mathematical equations, such as Coulomb's Law and the equations for electric potential and electric field, to calculate the desired values.

What are some common assumptions made when solving the Two nonconducting spheres problem?

Some common assumptions made when solving the Two nonconducting spheres problem include assuming that the spheres are point charges, meaning their size is negligible compared to the distance between them, and that they are isolated in space, meaning there are no other charges or objects nearby that could affect their behavior.

What are some real-world applications of the Two nonconducting spheres problem?

The Two nonconducting spheres problem has real-world applications in fields such as electrostatics, electromagnetism, and electrical engineering. It can also be used to model the behavior of charged particles in a variety of natural and man-made systems, such as atoms, molecules, and electronic circuits.

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