Calculate the resultant charge force with three charges on a circular surface // Applying Coulomb's Law with More Than Two Charges

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Greetings friends, back with more science content, for this occasion I bring you, how to calculate a circular surface, the resultant force with three point charges by applying Coulomb's Law for two or more charges, my friend, readers, have to take into account the basics , as the electric charge is a physical property of some subatomic particles, whose uniqueness is evidenced by forces of attraction and repulsion between them through electromagnetic fields, there are positive and negative charges, where opposite charges attract and equal charges they repel Then we have, my reader friends, what is fascinating about the law of the magnitude of each of the electric forces with which two point charges at rest interact, it is evident that this is directly proportional to the product of the magnitude of both charges and inversely proportional , since it is linked to the square of the distance that separates them and has the direction of the line that joins them, well for our case we have a circular surface as an example, but the detail if we draw the three load points gives us a right triangle , where q1=(-), q2=(+), and q3=(+).

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The relationship of the analysis will be the charge q1 and q2 are active my friend because they are opposite charges and also for the case of q1 and q3 they are active, since q2 and q3 are equally positive, considering that the force of interaction between two charges for q1 and q2, these double their magnitude if any of the charges doubles its fundamental base value.

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The first step is to identify the three boxes that originate a right triangle and we denote that q1 is a negative charge, q2 a positive charge and q3 a positive charge, which makes it attractive in the direction of q1 and q2, also for q3q1, Identify more then the right triangle for the charges and since we need to know the resultant, first we do the conversions of each of the charges to Coulomb and the distance takes the one in centimeters to meters. As we are going to use the law, we have the constant as additional data.

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Continuing with the solution of the problem then, we already have the conversion of the charges, the distance now only and we also have knowledge of the constant K , now what we do is as the resultant we name it F1, it would be the sum of that of the resultant f 2.1 and the other resultant would be f3.1. Another important piece of information when applying the formulas we have another equivalence of the vector u2,1= -j, since it will be a unit vector that goes in the opposite direction and direction to the y-axis, the same for the case of u3, 1, =i, with another letter because it goes in the opposite direction to the x axis, knowing that the three charges are in a vacuum.


We apply the formula for F2,1:

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We apply the formulas for F3,1 and the module.

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All images and gif were edited by my Samsung A23 phone


Bibliographical References


Basic electricity By David Arboledas Brihuega.


Electricity and magnetism By Germán Arenas Sicard, 2008.


Physics for science and technology. Electricity and..., Volume2,Part1 By Paul Allen Tipler, Gene Mosca, 2005.

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11 comments
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Interesting. I gave almost the same exercise to my second-year students. However, at the end I asked them to generalise the problem to a situation in which the triangle was completely arbitrary (so not a right triangle). And then I moved on with more complicated problems (more than three charges, before getting o the continuous case).

Note that I actually started with easier exercises (only two discrete charges, for instance and among others).

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Greetings teacher, it is very interesting to share these in reference to the loads, if you are right because over time we find a more complex case

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Just one question, you teach that in the university right?
!1UP

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If I teach, apart from economics and philosophy

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That look quite detailed in steps

Thank you for sharing

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