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Q.

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

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a

−λp2π∈0a

b

λp2π∈0a

c

−3λp4π∈0a

d

λp4π∈0a

answer is C.

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Detailed Solution

Field due to infinite line of charge E=λ2πε0r Electric dipole initially kept at the point A(a, 0, 0)Field E=λ2πε0aUi=−PEcosθAt (a, 0, 0), Uinitial=Pλ2π∈0  and (2a,0,0)  Ufinal=−Pλ2π∈0W=ΔU=Uinitial−Ufinal⇒W=−34λPπ∈0aW=−34λPπ∈0a
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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