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Question:

Consider the circular loop having current i and with central point O. The magnetic field at the central point O is

3μ₀i/7R acting downward

2μ₀i/3πR acting downward

5μ₀i/12R acting downward

6μ₀i/11R acting downward

Solution:

Magnetic field at the center due to the inner loop of radius R = (3/4) × μ₀I/2R downwards
Magnetic field at the center due to the outer loop of radius 3R = (1/4) × μ₀I/2(3R) downwards
Magnetic field at center due to the two straight wire segments is zero.
Hence net magnetic field at center of loop = (3μ₀I/8R) + (μ₀I/24R) downwards = 5μ₀I/12R downwards