Three point charges 1µC, -1µC, 2µC were initially infinite distance apart. Calculate the work done in assembling these charges at the vertices of an equilateral triangle of side 10cm.

Dear Student,
Given,
Three charges
q1=1μCq2=-1μCq3=2μC
are initially infinite distance apart and then brought at the vertices of an equilateral traingle of side r=10cm=0.1 m
​​​​​​Since, the potential energy of the three charges at infinite separation is 0, the work done in assembling these charges at the vertices of an equilateral triangle of side 10 cm is equal to the potential energy stored by the system of three charges for such a configuration.

Potential energy of the charge system when at the vertices of an equilateral triangle of side 10 cm is
U=14πεoq1q2r2+q2q3r2+q3q1r2U=9×1091×10-6×-1×10-60.12+-1×10-6×2×10-60.12+2×10-6×1×10-60.12U=9×109-1×10-10-2×10-10+2×10-10=9×109×-1×10-10=-0.9 J

So, work done by an external agent to bring the charges in such a configuration, W=-U=--0.9J=0.9 J.

​​​​​​Regards

 

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