The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density λ are kept parallel to each other. In there resulting electric field, point charges q and -q are kept in equilibrium between them. The point charges are confined to move in the x direction only. If they are given a small displacement about their equilibrium positions, then the correct statement(s) is (are)

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Both Charges execute simple harmonic motion.

Both charges will continue moving in the direction of their displacement.

Charge +q executes simple harmonic motion while charge -q continues moving in the direction of its displacement.

Charge -q executes simple harmonic motion while charges +q continues moving in the direction of its displacement.

answer is C.

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Detailed Solution

If +q is moved rightwards, if experiences net left ward force i.e. it returns to ‘O’.Hence the equilibrium is stable.If –q is moved rightwards, it experiences net force rightwards i.e., it does not return to O and continues to move rightwards.At a small displacement x from 'O', Enet=λ2πε01r−x−1r+xF=Enet q=λq2πε01r1−xr−1r1+xr=λq2πε0r1+xr−1−xr=λq2πε0r×2xr⇒F=λqπε0r2xF is leftwards, x is rightwards ⇒F∝−x.∴The particle executes SHM.

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