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NEET2026PhysicsChapterActual

A long conducting wire carrying a steady current I is bent into the shape shown in the figure. The configuration consists of two semi-infinite straight sections and a semi-circular arc of radius R centered at point O . What is the magnetic field at point O ?

Options

  1. A₀ I 4R [ 1 + 2 ] directed out of the page
  2. B₀ I 4R [ 1 - 2 ] directed out of the page
  3. C₀ I 4R directed out of the page
  4. D₀ I 4R [ 1 + 2 ] directed into the page

Correct answer

A. ₀ I 4R [ 1 + 2 ] directed out of the page

Step-by-step solution

The total magnetic field at the origin O is the vector sum of the magnetic fields produced by the three segments of the wire. For the top semi-infinite straight wire, the perpendicular distance from O is R . The magnetic field at O is given by B₁ = ₀ I 4 R . Using the right-hand rule, the direction is out of the page. For the semi-circular arc of radius R , the magnetic field at the center is half that of a full circular loop. Thus, B₂ = 1 2 ( ₀ I 2R ) = ₀ I 4R . Since the current flows counter-clockwise, the right

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