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Question

# Find the magnetic induction of the field at the point O of a loop with current I, whose shape is illustrated. A current I flows along a thin wire shaped as shown in figure. The radius of a curved part of the wire is equal to R the angle is 2ϕ. Find the magnetic induction of the field at the point O.

A
B=(πϕ+sinϕ)μ0I2πR
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B
B=(πϕ+tanϕ)μ0I2R
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C
B=(πϕ+tanϕ)μ0I2πR
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D
None of these
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Solution

## The correct option is C B=(π−ϕ+tanϕ)μ0I2πR We know that, Magnetic field due to circular arc at centre is Barc=μ0i4πRθ ⊗ Magnetic field due to given circular arc is B1=μ0I4πR(2π−2ϕ) B1=μ0I2πR(π−ϕ) ⊗ We know that, Magnetic field due to a line wire is given by, B=μ0I(sinθ1+sinθ2)4π(d) Here θ1=θ2=ϕ,d=Rcosϕ Magnetic field due to given straight wire B2=μ0I4πRcosϕ2sinϕ B2=μ0I2πRtanϕ ⊗ Net Magnetic field is Bnet=B1+B2 Bnet=μ0I2πR[π−ϕ+tanϕ]

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