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Question

Find the magnetic field at the centre O of the loop shown in the figure.
1152906_c6bb2732f0634a9d85a0b00db2c7e97c.png

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Solution

As point - O lies in - line with all three wires magnetic field due to them
B2=B4=B6=0

We know,

Barc= μoIθ4πR

So, B1=μoi4×4πR(π2)=μoi4×8R

B3=μoiπ4π(2R)=μoi8R

B5=μoi4π(R)(π2)=μoi8R

So, Bnet=n=10Bn=B1+B2+B3+B4+B5+B6

Bnet= 0+0+0+μoi8R[14+1+1]

Bnet=9μoi32R

1130636_1152906_ans_01199962475042b28224e068eee18217.png

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