Three point charges +q ,-2q and +q are placed at points (x = 0,y = a,z=0), (x = 0,y = 0, z = 0) and (x = a, y = 0, z = 0)
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Total potential energy of the system before shifting the charges was
q×2q4πε0l+2q×(−3q)4πε0l+(−3q)×q4πε0l=2q2−6q2−3q24πε0l=−7q24πε0l
Now if they are moved to the middle of the sides of the triangle the distances between them will be l2, so the total energy will be
q×2q4πε0l2/+2q×(−3q)4πε0l2/+(−3q)×q4πε0l2/=2(2q2−6q2−3q2)4πε0l=−14q24πε0l
So total work done is
W=−14q24πε0l−−7q24πε0l=−7q24πε0l
q×2q4πε0l+2q×(−3q)4πε0l+(−3q)×q4πε0l=2q2−6q2−3q24πε0l=−7q24πε0l
Now if they are moved to the middle of the sides of the triangle the distances between them will be l2, so the total energy will be
q×2q4πε0l2/+2q×(−3q)4πε0l2/+(−3q)×q4πε0l2/=2(2q2−6q2−3q2)4πε0l=−14q24πε0l
So total work done is
W=−14q24πε0l−−7q24πε0l=−7q24πε0l
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