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Question

Figure shows a closed loop AOCBA in which current I is flowing as shown. Given OA=OB=OC=a. Find the magnetic field at point B due to this loop.

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A
μ0I4π2a(^i+^k)
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B
μ0I4π2a(^j+^k)
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C
μ0I22πa(^j+^k)
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D
None of these
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Solution

The correct option is B μ0I4π2a(^j+^k)
At B, magnetic field will be zero due to CB and AB parts.
BAO=μ04πIa[sin0o+sin45o](^j)=μ0I4π2a^j
BOC=μ04πIa[sin0o+sin45o](^k)=μ0I4π2a^k
Net magnetic field at B
BAO+BOC=μ0I4π2a(^j+^k)

254445_167517_ans_66677570ee9a486f9e31631a258bd723.png

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