Identical +1.8 micro Colomb charges are fixed to adjacent corners of a square. What charge (magnitude and algebraic sign) should be fixed to one of the empty corners, so that the total electric potential at the remaining empty corner is 0V?

The problem is ambiguous. There are either a total of two charges or four charges. I should solve for the two possibilities.

When I solve for the sum of electric potential (Voltage $= k q/ r$) should one of the $r$ values be the diagonal length of the square?

If the $r$ value is not the diagonal length, should the $r$ value be only the length of the square?

How can the remaining corner have a specific charge that makes it's voltage 0? Does its charge change the voltage and charges at other corners of the square?

  • 2
    $\begingroup$ It says one of the empty corners (note the plural) which means there are 2 charges on 2 corners, not 4 on 4 corners (there wouldn't be any empty corners in this case anyway). $\endgroup$ – Kyle Kanos Sep 19 '14 at 16:32

Since this is a homework question, I will point you in the right direction rather than do your work for you.

Reading the question carefully, I believe you are trying to solve the following situation:

enter image description here

There is nothing ambiguous here. You have two "red" charges (identical, 1.8 uC), and need to determine the value of the "green" charge such that the potential at the "open" corner is zero.

Note that potential is a scalar, and can be added. Presumably the green charge has to be of opposite sign from the red ones so the potential can sum to zero. The distance of one of the charges is greater (by $\sqrt{2}$) than the other two. Take it from there.

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  • $\begingroup$ is voltage a quantity that occurs at a specific point or is it like a force that can influence other voltages around it? Can one voltage at a point decrease or cancel out the voltage at another point? $\endgroup$ – user57712 Sep 19 '14 at 17:03
  • $\begingroup$ Each charge creates a potential at every point in space. Think of it as the amount of work you have to do to take a point charge from infinity to that point in space. The potential can be positive or negative (do you push, or are you pulled). Because the equations are linear, you can use superposition. Total work done = (work done given just one charge at a time), summed over all charges. Voltage, in this sense, doesn't simply "exist at one point" - it can be defined at any point in space based on the charge distribution. You can't derive voltage at one place from voltage at another. $\endgroup$ – Floris Sep 19 '14 at 17:07
  • $\begingroup$ so electric potential is more like an electric field? $\endgroup$ – user57712 Sep 19 '14 at 17:13
  • $\begingroup$ Yes, except it is a scalar, not a vector. Actually the electric field is the gradient of the potential... $\endgroup$ – Floris Sep 19 '14 at 17:14
  • $\begingroup$ I can't add the voltages when I calculate the voltage for the green dot charge since I don't know what r value I should use for the green dot. I don't see why the red dots and green dots are placed in that formation. Why can't the red dots be placed diagonally from each other? $\endgroup$ – user57712 Sep 19 '14 at 17:23