Two identical conducting spheres are placed with centers .43 m apart. one is give a charge of +18x10^-6 and the other is given a charge of -14x10^-6. I know how to find the electric force but want to make sure of the rest.
a. If they are connected by a conducting wire, after equilibrium occurs, find the force on the two spheres.
b. How many excess protons are on one of the spheres after equilibrium?
a) After the two spheres are connected by a conducting wire, the charge will flow from the positive sphere to the negative until the charges on the spheres will be the same. Since the total charge is conserved, the new charge on each sphere will be
`(18*10^-6 + -14*10^-6)/2 = 2*10^-6`
(I assume the units of charge in your problem are Coulombs.)
Then, the electric force between the spheres will be
```F = k* (q_1*q_2)/r^2 = 8.99*10^9 * (2*10^-6 * 2* 10^-6)/(.43)^2 = 0.194 N`
b) To calculate the number of excess protons, recall that each proton has the change equal to the charge of electron, but positive: `1.6*10^-19` Coulombs.
Therefore, for the sphere (or any object), to be charged with a positive charge q, it must have `q/q_e` excess protons. Dividing the charge of the sphere by the electron charge, we get
`(2*10^-6)/(1.6*10^-19) = 1.25*10^13` , or 12,500,000 million excess protons.