Solving for Electron Transfer Between Charged Spheres

In summary: So if you remove x electrons from one sphere, you also have to add x electrons to the other sphere, so the total charge on each sphere is still n. In summary, the two small aluminum spheres, each with a mass of 0.0250 kilograms and separated by 80.0 centimeters, would require a transfer of 5.26682*10^15 electrons between them to create an attractive force of 1.00x10^4 N. This is because the total charge on each sphere must remain constant, even if a specific number of electrons is removed or added.
  • #1
Goldenwind
146
0
[SOLVED] Charged Spheres

Homework Statement


Two small aluminum spheres, each of mass 0.0250 kilograms, are separated by 80.0 centimeters. How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude 1.00x10^4 N (roughly one ton)? Assume that the spheres may be treated as point charges.


Homework Equations


F = kq1q2/r^2
q = ne


The Attempt at a Solution


In a previous question, it was worked out that each sphere has 7.25x10^24 electrons. It's confirmed that this answer is correct.

F = kq1q2/r^2.

We're taking an amount from the first, and giving it to the second. I declared variable 'x' to be this amount. Since each sphere has the same number of electrons, we can use a common variable 'n', instead of n1 and n2.

F = kq1q2/r^2
F = k(ne)(ne)/r^2
F = k((n-x)e)((n+x)e)/r^2, introducing the variable x, taking x electrons from one, and giving them to the other, then solving for F = 10^4.

Fr^2/k = e^2(n^2 - x^2)
Fr^2/(ke^2) = n^2 - x^2
(Fr^2/(ke^2)) - n^2 = -x^2
-(Fr^2/(ke^2)) - n^2 = x^2
Sqrt(-(Fr^2/(ke^2)) - n^2) = x

Sqrt(-((10000)(0.8)^2/((8.988*10^9)(1.60217646*10^-19)^2)) - (7.25*10^24)^2) = x
x = Not a real value.
I took the absolute value of the huge number above before square rooting, and it came out to 7.25*10^24... which would mean that x = n, therefore to give the said force, 100% of the electrons would need to be transfered.

I tried this answer, and was told I was wrong.
 
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  • #2
One can just assume that [itex]q_1=n e = -q_2 [/itex].

Remember that the charge on an electron is negative.
 
  • #3
Kurdt said:
One can just assume that [itex]q_1=n e = -q_2 [/itex].

Remember that the charge on an electron is negative.
Not too too sure that I follow what you mean, but I'll try flipping the e value.

Sqrt(-(Fr^2/(ke^2)) - n^2) = x
Sqrt(-((10000)(0.8)^2/((8.988*10^9)(-1.60217646*10^-19)^2)) - (7.25*10^24)^2) = x

Still a non-real result (Root of a negative). Taking absolute value just to see what I get.
Got same answer, 7.25*10^24.
I understand getting the wrong answer, but I do find it weird that x = n, exactly...
 
  • #4
What I was getting at was if you work from the following you should get a sensible answer.

[tex] F=k\frac{-n^2e^2}{r^2} [/tex]
 
  • #5
Kurdt said:
What I was getting at was if you work from the following you should get a sensible answer.

[tex] F=k\frac{-n^2e^2}{r^2} [/tex]

F = -kn^2*e^2 / r^2
Sqrt(-Fr^2/(ke^2)) = n
Sqrt(-(10000)(0.8)^2/((8.988*10^9)(-1.60217646*10^-19)^2)) = n
n = 5.26682*10^15

Trying...
Correct answer.

Just curious though, what did I do wrong? Why did my (n-x)(n+x) theory not work?
Oooh... it would take 5.26682*10^15 electrons to cause force F... blah.
Thank-you for your time :)

/solved.
 
  • #6
The n-x and n+x approach didn't work because these are just the numbers of electrons on each sphere. What you want is the number that is contributing to the force.
 

1. What are charged spheres?

Charged spheres are objects that have an excess or deficiency of electrons, resulting in a net positive or negative charge. This charge creates an electric field around the sphere which can interact with other charged objects.

2. How are charged spheres created?

Charged spheres can be created through various methods such as friction, induction, or contact with other charged objects. For example, rubbing a balloon against your hair can transfer electrons and create a negatively charged sphere.

3. What is the significance of charged spheres in physics?

Charged spheres play a crucial role in many areas of physics, including electrostatics, electromagnetism, and quantum mechanics. They help us understand electric fields, forces, and potential energy.

4. Can charged spheres exist in isolation?

No, charged spheres cannot exist in isolation as they will always interact with their surroundings, either by attracting or repelling other charged objects. However, they can be shielded from external fields to reduce their interactions.

5. How are charged spheres used in practical applications?

Charged spheres have many practical applications, such as in electrostatic precipitators, where they are used to remove pollutants from air. They are also used in electrophoresis, a technique for separating and analyzing molecules. In addition, charged spheres are used in electronic devices, such as capacitors, to store and release electric energy.

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