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Question

A wire loop formed by joining two semi-circular wires of radii R1 arid R2 carries a current as shown in the adjoining diagram. The magnetic induction at the centre O is :
334185_d08eb36322934af3ad67a9d797868746.png

A
μ0Iπ4πR1
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B
μ0Iπ4πR2
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C
μ0Iπ4π(1R11R2)
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D
μ0Iπ4π(1R1+1R2)
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Solution

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×107N/Am.
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).

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