A wire loop PQRSP is constructed by joining two semi-circular coils of radius r1 and r2 respectively, as shown in the figure. If the current flowing in the loop is I, then the magnetic induction at the point O is:
A
μ0I4[1r1−1r2]
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B
μ0I4[1r1+1r2]
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C
μ0I2[1r1−1r2]
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D
μ0I2[1r1+1r2]
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Solution
The correct option is Aμ0I4[1r1−1r2]
Magnetic field due to coil of radii r1 →B1=12×μ0I2r1 out of plane Magnetic field due to coil of radii r2 →B2=12×μ0I2r2⊗ in of plane B∝1r hence →Bnet=μ0I4r1−μ0I4r2 ⇒μ0I4(1r1−1r2)