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An infinitely long positively charged straight thread has a uniform linear charge density . An electron revolves along a circular path having its center on the axis of the wire. The graph that correctly represents the variation of the angular momentum ( L ) of the electron as a function of the radius ( r ) of its circular path is best described as :

Options

  1. AA horizontal straight line parallel to the r -axis
  2. BA parabola passing through the origin ( L r^2 )
  3. CA curve representing L r
  4. DA straight line passing through the origin with a positive slope

Correct answer

D. A straight line passing through the origin with a positive slope

Step-by-step solution

Electric field E at a distance r due to an infinitely long wire is E = 2 ₀ r . The electrostatic force on the electron provides the necessary centripetal force: F_e = eE = e 2 ₀ r Equating this to the centripetal force: mv^2 r = e 2 ₀ r Solving for velocity v : v = e 2 ₀ m This shows that the orbital velocity v is independent of the radius r (i.e., v is constant). The angular momentum of the electron is given by: L = mvr Since m and v are constants, L r . Therefore, the graph of L versus r is a straight line passin

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