A very long wire ABDMNDC is shown in figure carrying current I. AB and BC parts are straight, long and at right angle. At D wire forms a circular turn DMND of radius R. AB, BC parts are tangential to circular turn at N and D. Magnetic filed at the center of circle is:

Step-by-step solution

B 0 → = B 0 → 1 + B 0 → 2 + B 0 → 3 + B 0 → 4 μ 0 i 4 π R sin ⁡ 90 ° - s i n 45 ° ⨂ + μ 0 i 2 R ⨀ + μ 0 i 4 π R ( s i n 45 ° + s i n 90 ° ) ⨀ - μ 0 i 4 π R 1 - 1 2 + μ 0 i 2 R + μ 0 i 4 π R 1 2 + 1 ⨀ = μ 0 i 4 π R - 1 + 1 2 + 2 π + 1 2 + 1 ⨀ = μ 0 i 4 π R 2 + 2 π ⨀ = μ 0 i 2 π R 1 2 + π ⨀