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A wire is bent in the form of a circular arc with a straight portion AB. Magnetic induction at O when current I is flowing in the wire, is

a
μ02r π−θ + tanθ
b
μ02πr π+θ − tanθ
c
μ0I2πr π−θ + tanθ
d
μ0I2πr −tanθ+π−θ

detailed solution

Correct option is C

BAB = μ0I4πOC  2 sin θBut  OC=r cos θor  BAB = μ0I2πr tan θMagnetic field due to circular portion,BAB' =   μ0I2r2π−2θi2π = μ0I2πr  π−θTotal magnetic field=μ0I2πr  tan θ  +  μ0I2πrπ−θ=μ0I2πr  tan θ  + π−θ

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