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JEE MainPhysicsMagnetic Effects of Current

A long straight coaxial cable consists of a solid inner cylindrical conductor of radius R₁ carrying a steady current I , and a thin outer cylindrical shell of radius R₂ carrying the same current I in the opposite direction. Which of the following correctly describes the variation of the magnitude of the magnetic field B as a function of the radial distance r from the central axis?

Options

  1. AB decreases as 1/r for 0 R₂
  2. BB increases linearly with r for r R₂
  3. CB increases linearly with r for r R₂
  4. DB increases linearly with r for r R₂

Correct answer

B. B increases linearly with r for r R₂

Step-by-step solution

According to Ampere's circuital law, B d l = ₀ I_ enc . For r For R₁ For r > R₂ (outside the cable), the net enclosed current is I - I = 0 . Thus, B(2 r) = 0 B = 0 . Therefore, B increases linearly for r R₂ . Answer: B increases linearly with r for r R₂

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