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Find the magnetic field at the point P in figure. The curved portion is a semicircle and the straight wires are long

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a
μ0i2d1+2π
b
3μ0i2d1+2π
c
5μ0i2d1+2π
d
7μ0i2d1+2π

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detailed solution

Correct option is A

The magnetic field at P due to any current element in the figure is perpendicular to the plane of the figure and coming out of it. The field due to the upper straight wire is B1=12×μ0i2πd2=μ0i2πd
Same is the field B2 due to the lower straight wire. The field due to the semicircle of radius (d/2) is Ba=12×μ0i2d2=μ0i2d
The net field is   B=B1+B2+Ba=μ0i2d1+2π. 
 

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