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 :

Question

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 :, B → = μ 0 4 π I R π i ^ + 2 k ^, B → = - μ 0 4 π I R π i ^ - 2 k ^, B → = - μ 0 4 π I R π i ^ + 2 k ^, B → = μ 0 4 π I R π i ^ - 2 k ^

MARKS App · Accepted Answer

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 → 2 + B → 3 B c = - μ 0 I 4 R i + 2 k ^ π = - μ 0 I 4 π R ( π i ^ + 2 k ^ )

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