Magnetic Field

Step 1: Concept
Field due to a straight wire of infinite length is if the point is on a line perpendicular to its length while at the centre of a semicircular coil is .
Step 2: Analysis
The total magnetic field at O is the vector sum of fields due to the two straight sections ( and ) and the semicircular section ( ).
Step 3: Calculation
$ (\frac{\mu_{0}}{4\pi})(\frac{i}{r})(\pi+2)$ out of the page.
Final Answer: (B)

Concept: Magnetic field due to finite wire:

Step 1: Geometry
Distance from centre to side:

Step 2: Field due to one side


Step 3: Total field (4 sides)
Conclusion:

Step 1: Understanding the Concept:
Magnetic moment: . Same wire length different areas for square and circle.
Step 2: Detailed Explanation:
Let total wire length . For square: , . For circle: , . Ratio of magnetic moments: .
Step 3: Final Answer: