# Calculating the number of electrons given the force of repulsion

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?

haruspex
Homework Helper
Gold Member
2020 Award
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?

Doc Al
Mentor
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".