Calculating the number of electrons given the force of repulsion

AI Thread Summary
To determine the number of excess electrons on two charged spheres repelling each other with a force of 3.33×10^−21N, the equation F=kq/(r^2) is used, where k is Coulomb's constant and r is the distance between the spheres. After calculating the charge (q) required for the given force, a value of 1.48x10^-31 C was obtained, which led to confusion regarding the appropriate number of electrons. By applying Coulomb's Law correctly, the calculation yielded approximately 578,125 electrons per sphere. It was suggested to define the charge on each sphere in terms of the number of electrons to clarify the calculation. The final conclusion is that each sphere requires 578,125 excess electrons to achieve the specified force of repulsion.
tmichaud26
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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?
 
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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".
 
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