What third charge should be placed at x=+26cm so that the total electric field at x=+13.0cm is zero?

What third charge should be placed at x=+26cm so that the total electric field at x=+13.0cm is zero?

Express your answer to three significant figures and include appropriate units"

Let's call A the point at x=+13 cm where the total electric field is zero.

First of all, we can calculate the total field generated by the two charges  and . The two charges have a distance from point A of  and , respectively. The field generated by the positive charge heads towards right in point A, while the one generated by the negative charge heads towards left, so we should consider a sign - on this field. Therefore, the total field generated by charge 1 and 2 in A is

In order to have total net field of zero in point A, the field generated by charge 3 should be equal to this value, and should point towards the left, so it must be a positive charge. So, we have:

where  is the distance of the charge 3 from point A. So we find

this is a good question! i'll do some research and come back when i have the answer!

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