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Question

A current I flows in the anticlockwise direction through a square loop of side a lying in the xoy plane with its center at the origin. The magnetic induction at the center of the square loop is

A
22μ0Iπa^ex
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B
22μ0Iπa^ez
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C
22μ0Iπa2^ez
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D
22μ0Iπa2^ex
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Solution

The correct option is B 22μ0Iπa^ez
Field due to one side of loop at O
=4.μI4π(a2)(2sin450)
Field at O due to all four sides is along unit vector ¯ez
Total field
=4.μI4π(a2)(2sin450)=22μ0Iπa
651830_617143_ans_3d9cd868f87545b7ba28ea0ff08e7a43.png

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