two concentric rings of radii `r` and `2r`are placed with centre at origin. Tow charges ` +q` each are fixed at the diametrically opposite points of the rings as shown in figure . Smaller ring is now rotated by an angle ` 90^@` about Z-axis then it is again rotated by ` 90^@` about Y-axis . Find the work done by electrostatic forces in each step . If finally larger ring is rotated by `90^@` about X-axis , find the total work required to perform all three steps .
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Answer

`W_("first step")=(8/3-4/sqrt(5))(Kq^(2))/r, W_("second step")=0, W_("total")=0`

Explanation

P.E. of outer ring charges does not change
`=(Kq^(2))/Rxx2+(Kq^(2))/(3R)xx2=(8Kq^(2))/(3R), U_(f)=(Kq^(2))/(sqrt(5)R)xx4`
Hence `W_("electron")=-DeltaU`
`W_("electron")=-(V_(f)-V_(i))=-(Kq^(2))/R[4/sqrt(5)-8/3]=(Kq^(2))/R[8/3-4/sqrt(5)]`