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
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a
μ02r π−θ + tanθ
b
μ02πr π+θ − tanθ
c
μ0I2πr π−θ + tanθ
d
μ0I2πr −tanθ+π−θ
answer is C.
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Detailed Solution
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