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NEET2015PhysicsMagnetic Effects of CurrentActual

A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X -axis while semicircular portion of radius R is lying in Y - Z plane. Magnetic field at point O is :

Options

  1. AB → = μ 0 4 π I R π i ^ + 2 k ^
  2. BB → = - μ 0 4 π I R π i ^ - 2 k ^
  3. CB → = - μ 0 4 π I R π i ^ + 2 k ^
  4. DB → = μ 0 4 π I R π i ^ - 2 k ^

Correct answer

C. B → = - μ 0 4 π I R π i ^ + 2 k ^

Step-by-step solution

B → c       =       B → 1 + B → 2 + B → 3 . B 1     =       μ 0 4 π R       sin ⁡ 90 + s i n θ - k ^ B 1     =       μ 0 4 π R       - k ^ = B 3 B due to segment 2 B 2   =       μ 0   I 4 π × π ( - i ^ ) = - μ 0 I 4 R i ^ So B at center       B → c =   B → 1 +   B &#8

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