# Problems about Electricity and Magnetism

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I apologize, I wrote all of this out in a word processor before attempting to post it and I did not notice that there is a template for giving problems. I hope you forgive me, my posts tend to be wordy and take awhile to write; attempting to write it in the text box would result in the server logging me out. The information required is all here, though. At least, that I think so.

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.

## Answers and Replies

cupid.callin
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?

When two bodies are connected, their potential becomes 0
hence in this case charge will be divided equally. but donot consider that same will happen if the radii were different

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)

Does the problem specify from which charge the distance has to be calculated?

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Does the problem specify from which charge the distance has to be calculated?

No. What I gave you is exactly what I was given.

Thank you for your assistance on the first problem, though. It has been very helpful to me.

cupid.callin
No. What I gave you is exactly what I was given.

Thank you for your assistance on the first problem, though. It has been very helpful to me.

Are you getting an answer 1.121 cm ???????

I an getting different answer. SPAMSPAMSPAM
Are you getting an answer 1.121 cm ???????

I an getting different answer. Because I managed to solve the equation down to a polynomial, one of the second degree, I actually had multiple solutions as most polynomials tend to have. The answers I had, after solving the equation, are d = 0.266 and d = 1.121.
In this equation, Fe = Ke * (q1*q2)/(d^2) d must be an amount in meters in order for the results to be correct. This means that the answers are, as I have found them, 26.6 cm and 112.1 cm.
What answers are you getting?

cupid.callin
I'm getting only 26.6
as both charges are negative, E at 112.1 cannot be 0 .... (Why?)

the answer must be 26.6cm or 43-26.6 = 16.4cm

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Thank you. It turns out that the answer must be in centimeters, and not meters. I just inputted 26.6, instead of 0.266, and the system took that answer. I have no idea how my teacher thought that the students would now which to input, but then again I'm not sure if he made the problems.

cupid.callin
But still ask your teacher not do deduct marks as its not your fault!!!
Students are supposed to answer in SI when unit of answer is not specified!!!!!!!!!!