An infinitely long positively charged straight thread has a linear charge density λ C m⁻¹. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is:
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Question

An infinitely long positively charged straight thread has a linear charge density λ C m⁻¹. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is:

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G1 Physics · Accepted Answer

Electric field at distance r from an infinitely long line charge: E = 2kλ/r Force on electron: F = eE = 2kλe/r This force provides centripetal force: mv²/r = 2kλe/r Therefore: v² = 2kλe/m Kinetic energy: KE = ½mv² = ½m(2kλe/m) = kλe Thus kinetic energy is independent of r. Therefore, the KE-r graph is horizontal. Hence, Image 2 is correct.