# Calculating the number of electrons given the force of repulsion

• tmichaud26
In summary, the conversation discusses the calculation of the number of excess electrons needed on two small spheres with equal charge in order to produce a force of repulsion of 3.33×10^−21N when spaced 20.0 cm apart. The equations used include Coulomb's Law (F=kq/(r^2)) and the charge of an electron (e=-1.6X10^-19 C). After some trial and error with different equations, the final solution involves assuming that each sphere has the same number of electrons (n) and rewriting the equation in terms of that variable to solve for n. The final answer is 578,125 electrons needed on each sphere.
tmichaud26
Homework Statement
Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 3.33×10^−21N?
Relevant Equations
Charge of an electron e=-1.6X10^-19 C
F=kq/(r^2)
Homework Statement: Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 3.33×10^−21N?
Homework Equations: Charge of an electron e=-1.6X10^-19 C
F=kq/(r^2)

For this I set the force equal to 3.33X10^-21N and solved for the value of q given that we know the values for k (9x10^9Nm^2/C^2) and r=0.2m. This gave a q value of 1.48x10^-31 which I then divided by the charge of an electron to get a value of 9.25x10^-14 which is not an appropriate value for number of electrons. Am I using the correct equation?

tmichaud26 said:
F=kq/(r^2)
Something missing there?

Do I need to include the r-vector?

This time I set F=3.3x10^-21 and divided this by the right side of the equation which I calculated out to be (9x10^9)(1.6x10^-19)(1.6x10^-19)/(.2x.2) which gave me a value of 578,125 electrons. Do I need to divide this value by 2 to get the number of electrons that need to be present on each sphere or does each sphere need 578,125 electrons?

Try this: Assume that each sphere has the same number of electrons, let's call that number "n". So, if the charge on each electron is "e", what's the charge on each sphere? Rewrite your equation in terms of that, then you can solve for "n".

## What is the formula for calculating the number of electrons given the force of repulsion?

The formula for calculating the number of electrons in a system given the force of repulsion is: n = F/(kq2), where n is the number of electrons, F is the force of repulsion, k is Coulomb's constant, and q is the charge of each electron.

## What is Coulomb's constant and what is its value?

Coulomb's constant, denoted by k, is a proportionality constant that relates the force of repulsion between two charged particles to their charges and the distance between them. Its value is approximately 8.99 x 109 N·m2/C2.

## Can the number of electrons and the force of repulsion be directly proportional?

Yes, the number of electrons and the force of repulsion are directly proportional. This means that as the force of repulsion increases, the number of electrons also increases, and vice versa. This relationship is described by the formula n = F/(kq2).

## What units are used for the force of repulsion and the number of electrons?

The force of repulsion is measured in Newtons (N) and the number of electrons is a unitless quantity. However, in some cases, the number of electrons may be expressed in terms of moles (mol).

## Can this formula be used to calculate the number of electrons in any system?

No, this formula can only be used to calculate the number of electrons in a system where the force of repulsion is the only significant force acting on the electrons. In other systems, such as those with additional forces or non-point charges, this formula may not accurately calculate the number of electrons.

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