What is the work required to arrange charged objects in a right triangle?

AI Thread Summary
To calculate the work required to arrange charged objects at the corners of a right triangle, one must consider the initial positions of the charges being very far apart. The potential energy of the system can be determined using the formula W = Fed = qEd, where q represents the charge and d the distance. The specific dimensions of the triangle include one side measuring 12 cm and the other 19 cm, with the hypotenuse calculated at 22.5 cm. The process involves bringing the charges in sequentially from infinity, calculating the electric field E(r) for each charge, and integrating the work done for the final charge based on the superposition of the other two charges. This methodical approach allows for the accurate determination of the total work required for the arrangement.
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Homework Statement



How much work does it take for an external force to set up the arrangement of charged objects in the diagram on the corners of a right triangle? Assume that q = -5.2 µC, that d = 19 cm, and that the three objects are initially very far away from each other.

Homework Equations



W=Fed =qEd


The Attempt at a Solution


I have no clue how to start. I figured out the potential to be -1.15, I just need a nudge in the right direction
 
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Bring the charges in from infinity, one at a time?

'd' does not completely specify a right triangle.
 


one of the sides is 12 cm (y axis). The other side (d) is 19 cm (x axis). The hypotenuse is 22.5. I couldn't load the pic onto this website
 


also charge 1 is 5.5e-6C charge 2 is -5.2e-6C and charge 3 is 2.5e-6 C
 


Find the work by integration

W =\int{eE(r)dr}

To start, put one charge at its vertex, find E(r) for the charge. Bring another charge to it's vertex, integrating the work.

For the last charge, the work done is the superposition due to the other two charges.
 
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