The correct option is D μ0Iπ4π(1R1+1R2)
Answer is D.
Circular wire produces magnetic field inside the circle and outside the circle. Magnetic field around a circular wire is calculated by the formula;B=μ0I2rwhere,μ0=4π×10−7N/A−m.
since we have semicircle of radius R1 below, we put 1/2 in front of our formula.
The formula becomes μ0Iπ4πR1.
Similarly, we have semicircle of radius R2 above, we put 1/2 in front of our formula.
The formula becomes μ0Iπ4πR2.
Therefore, μ0Iπ4πR1 + μ0Iπ4πR2
That is, the magnetic induction at the centre O is given as μ0Iπ4π(1R1+1R2).