Magnetic field due to the current carrying wire as shown in the figure at point "O" will be:

CONCEPT:

• The Current-Carrying Conductor produces a magnetic Field Around it. 

Biot-Savarts Law: 

The direction and Magnitude of this magnetic field can be obtained from Biot-Savarts Law. 

Where dB = Magnetic Field produced due to small wire of length dl, I = Current in wire, μ0 = Permittivity of free space, dl = Small Current Element

• The magnetic field generated due to the current-carrying circular conductor at its center is given as:

• This result has been obtained from Biot Savarts Law.

EXPLANATION:

• The Magnetic Field Produced due to the Semi-Circular wire is half of that of Circular wire.
• So, the magnetic field produced at the center "O" of the wire will be

Hence option 2 is the correct option.