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# Electrostatics: Coulomb's law, Resultant force

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There are 3 electrostatic charges q1=-1Q, q2=2Q and q3=1Q. These charges are placed as follows: q2 is placed at the origin, q1 is placed at a distance +B from the origin on the positive y axis and charge q3 is placed a distance +B from the origin on the positive x axis.

Find the force (magnitude and direction) on q3 due to q1 and q2. Please give the answer in vector notation (Cartesian coordinates)

https://brainmass.com/physics/coulombs-law/electrostatics-coulombs-law-resultant-force-294531

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There are 3 electrostatic charges q1=-1Q, q2=2Q and q3=1Q. These charges are placed as follows: q2 is placed at the origin, q1 is placed at a distance +B from the origin on the positive y axis and charge q3 is placed a distance +B from the origin on the positive x axis.
find the force (magnitude and direction) on q3 due to q1 and q2. Please give the answer in vector notation (Cartesian coordinates)

The situation is shown in the diagram.
Coulomb's law gives the force between two point charges. According to this the magnitude of the force between to charges q1 and q2 at a distance r from each other is given by

The direction of this force is along the line joining the two charges and repulsive if the charges are similar and attractive if the charges are opposite.
In vector form the force on charge q2 due to charge q1 can be written as

Here is the position vector of charge q2 relative to q1.
Thus the force on q3 due to charge q2 is given by

And the force on q3 due to q1 is given by

Here and are unit vectors in x and y directions respectively.

Hence the resultant force on q3 is given by

Or
Or
Or
Or
Hence magnitude of the force is given by

Or
And its direction with x axis is given by

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!