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Determine the interaction energy of the ...

Determine the interaction energy of the point charges located at the corners at the corners of a square with the side `a` in the circuit shown in Fig.

Text Solution

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The interaction energy of an assembly of charges is given by
`(1)/(4piepsilon_(0))underset(i nej)overset(n)sum(q_(i)q_(j))/(r_(ij))`
`therefore U=U_(12)+U_(13)+U_(14)+U_(23)+U_(24)+U_(34)`
`=-(kq^(2))/(a)+(kq^(2))/((sqrt(2a)))-(kq^(2))/(a)-(kq^(2))/(a)+(kq^(2))/((sqrt(2a)))-(kq^(2))/(a)`
`=-(sqrt(2)kq^(2))/(a)[2sqrt(2)-1]`
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