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(A) The wire consists of three sections: $(i)$ a straight semi-infinite wire,(ii) a semicircular arc of radius $R$,and (iii) another straight semi-inf

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$\frac{\mu_0 I}{4 R}$

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(A) The wire consists of three sections: $(i)$ a straight semi-infinite wire,(ii) a semicircular arc of radius $R$,and (iii) another straight semi-infinite wire.For section $(i)$,the point '$O$' lies on the axis of the wire,so the magnetic field $B_1 = 0$.For section (iii),the point '$O$' also lies on the axis of the wire,so the magnetic field $B_3 = 0$.For section (ii),the magnetic field at the center of a semicircular arc is given by $B_2 = \frac{\mu_0 I}{4 R}$.Therefore,the total magnetic field at '$O$' is $B = B_1 + B_2 + B_3 = 0 + \frac{\mu_0 I}{4 R} + 0 = \frac{\mu_0 I}{4 R}$.

$A$ wire has three different sections as shown in the figure. The magnitude of the magnetic field produced at the centre '$O$' of the semicircle by the three sections together is $(\mu_0 = \text{permeability of free space})$:

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