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Question

In the figure shown, the magnetic field induction as the point O will be
617671_d751ce3e64d349d496d366ff714eb82f.png

A
μ0i2πr
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B
(μ04π)(ir)(π+2)
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C
(μ04π)(ir)(π+1)
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D
μ0i4πr(π2)
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Solution

The correct option is B (μ04π)(ir)(π+2)
Field due to a straight wire of infinite length is μ0i4πr if the point is on a line perpendicular to its length while at the centre of a semicircular coil is μ0πi4πr
B=Ba+Bb+Bc
=μ04πir+μ04ππir+μ04πir
=μ0i4πr(π+2) out of the phase
653667_617671_ans_035a5bf38d3240b681d95050670c04e8.png

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