What will be the magnetic field at point P in the figure below ?

Question

TestHub · Accepted Answer

The magnetic field at P is the sum of fields from the semicircular arc and the two straight wires.

For the semicircular arc: $B_{1} = \frac{μ _{0} i}{4 R}$ .

For the two straight wires: $B_{2} = 2 \times \frac{μ _{0} i}{4 π R}$ .

Total field: $B = B_{1} + B_{2} = \frac{μ _{0} i}{4 R} + \frac{μ _{0} i}{2 π R} = \frac{μ _{0} i}{4 R} (1 + \frac{2}{π})$ .

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