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Due to Inconvenient circumstances, I am currently unable to receive assistance on these problems from my teacher. I have known of the existence of these forums for a while, from browsing the internet for help on other work, and I have decided to create an account and see if anyone here can help me.

The first problem I have seems to be a simple one, however my teacher has not gone over how to complete this so I am left mostly in the dark. The problem states:

*Two identical conducting spheres are placed with their centers 0.4 m apart. One is given a charge of +1.3 * 10^-8 C and the other a charge of -1.1 * 10^-8 C. The spheres are then connected by a conducting wire. After equilibrium has occurred, find the electric force between the two spheres.*

I assume that equilibrium is referring to the moment in which the electrons are balanced throughout the objects. If this is the case the solution would be simple; firstly, I would need to add the charges of the spheres together. This will give me the resultant charge throughout the entire object. Then I would need to divide this amount by two, in order to estimate the charge each individual sphere holds. Of course, the volume and composition of the wire is not given so it has to be assumed that I should not take into account any charge the wire holds. In any case, I would then take this charge and plug it into the equation Fe = Kc X (q1*q2)/(d^2), where the single charge would be both q1 and q2, as after equilibrium (or after what I am assuming equilibrium is) the charges of both of the spheres should be identical.

And yet, I am unsure whether or not the above algorithm is correct. So, is my method correct?

The second problem involves magnetism directly. It states:

*A charge q1 of -5.00 X 10^-9 C and a charge q2 of -1.9 X 10^-9 C are separated by a distance of 43 cm. Find the equilibrium position for a third charge of +20.0 X 10^-9. (Yes, +20.0 X 10^-9 is what the problem states)*

Now, equilibrium here I believe means that I must find the distance between charges q1 and q2 in which the electric forces on the third charge are equal. In this case, I would have to set up an equality:

Kc * (q1*q3)/(d^2) = Kc * (q2*q3)/( (0.43-d)^2)

After this, I must attempt to solve for d using this process:

(q1*q3)/(d^2) = (q2*q3)/( (0.43-d)^2)

q1*q3*(0.43-d)^2 = d^2*q2*q3 (cross multiplication)

-1*10^(-16)*d^2 + 8.6*10^(-17)*d - 1.849*10^(-17) = -3.8*10^(-17)*d^2

-6.2*10^(-17) + 8.6*10^(-17)*d - 1.849*10^(-17) = 0

d = ~0.266 or d = ~1.121 (from the Quadratic formula)

Now, it must be said that my teacher is having his students input the answers into an online system instead of simply writing the answers on paper and giving that paper to him. When an incorrect solution is inputted, the answer is not taken and points are reduced from the final grade. That is, I can only receive credit if my answers are correct and then the amount of credit is determined by how many incorrect solutions are inputted before the correct one. I attempted to use the first answer, as it is the only one between 0 and 0.46 (the distance allotted in the problem) and the system told me that the answer was incorrect. I have looked through this problem and at least tried to verify it but still I receive that same answer. I might have incorrectly typed the answer into the system, however I want someone to critique my method before I take any more action.