Magnetic Field Due to Current through a Circular Loop
A wire loop i...
Question
A wire loop is formed by joining two semi-circular wires of radii R1andR2 carrying current I as shown in the given diagram. The magnitude of net magnetic field at the centre O is
A
μ0lπ4πR1
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B
μ0lπ4πR2
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C
μ0lπ4π[1R1−1R2]
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D
μ0lπ4π[1R1+1R2]
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Solution
The correct option is Dμ0lπ4π[1R1+1R2] Magnetic field due to current carrying semi-circular loop at the centre, B=μ0/π4πr, where l is the current through the loop and r is the radius of the loop. ∴ Magnetic field at the centre O due to semi-circular loop of radius R1,B1=μo/π4πR1
Magnetic field at the centre O due to semi-circular loop of radius R2,B2=μo/π4πR2
The magnetic field due to part of wire RS and PQ is zero. ∴ Net magnetic field at the centre, Bnet=B1+B2+B2+0+0 =μo/π4π(1R1+1R2)
Hence, the correct answer is option (4).