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Q.

Find the magnetic field at the centre of the circular loop as shown in the figure, when a single wire is bent to form a circular loop and also extends to form straight sections.

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a

μ0I2R ⊙

b

μ0I2R  1+1π2⊙

c

μ0I2R  1−1π2⊗

d

μ0IR  1−1π2⊗

answer is B.

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Detailed Solution

Magnetic field due to AB,B→1  =  μ0I4πR  sin π2−sin π4⊗=  μ0I4πR  1−12 ⊗Magnetic field due to circular loop,B→2=  μ0I4R ⊙Magnetic field due to straight wire BC,B3=  μ0I4πR sin π2+sin π4⊙=  μ0I4πR1+12 ⊙  B→  =B→1 + B→2  +  B→3= μ0I2R + 2μ0I4πR − 12 ⊙ = μ0I2R 1+12 π ⊙
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Find the magnetic field at the centre of the circular loop as shown in the figure, when a single wire is bent to form a circular loop and also extends to form straight sections.