An infinite line charge of uniform charge density λ is held fixed along the $$Z-axis$$ of a Cartesian coordinate system. A point electric dipole initially kept at the point $$A(+a$$, $$0$$, $$0)$$ with the dipole moment P→ along the negative $$X-direction$$ is moved to the point $$B(2a$$,$$0$$,$$0)$$ and rotated so that its dipole moment along positive x direction. The work done by the external agent on the dipole in the entire process is

Question

An infinite line charge  of uniform charge density λ      is held fixed along  the $$Z-axis$$ of a Cartesian coordinate system. A point electric dipole  initially kept at the point $$A(+a$$, $$0$$, $$0)$$ with the dipole moment P→      along the negative  $$X-direction$$ is moved to the point $$B(2a$$,$$0$$,$$0)$$ and rotated so that its dipole  moment along positive x direction. The work done by the external agent on the  dipole in the entire process is

Infinity Learn · Accepted Answer

Field due to infinite line of charge $$E=$$λ$$2$$πε$$0r$$ Electric dipole initially kept at the point $$A(a$$, $$0$$, $$0)Field$$ $$E=$$λ$$2$$πε$$0aUi=$$−PEcosθAt (a$$, $$0$$, $$0), $$Uinitial=P$$λ$$2$$π∈$$0$$  and (2a$$,$$0$$,$$0)  $$Ufinal=$$−Pλ$$2$$π∈$$0W=$$Δ$$U=Uinitial$$−Ufinal⇒$$W=$$−$$34$$λPπ∈$$0aW=$$−$$34$$λPπ∈$$0a$$

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