Q.

A wire carrying current i has the configuration shown in figure. Two semi-infinite straight sections, each tangent to the same circle, are connected by a circular arc, of angle θ, along the circumference of the circle, with all sections lying in the same plane. What must θ (in rad) be in order for B to be zero at the center of circle?

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answer is 2.

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Detailed Solution

Magnetic field at O due to wire 1 isB→1=μ0i4πR⊙ and that due to wire 2 is B→2=μ0i4πR⊙⇒B→=B→1+B→2=μ0i2πR⊙ Magnetic field at the centre due to circular arc subtending angle θ at the centre is given byB→arc=μ0i2Rθ2π⊗ If B→net =0⇒B→+B→arc =0 ⇒  B→=-B→arc  ⇒  μ0i2πR⊙=-μ0i2Rθ2π⊗ ⇒  μ0i2πR=μ0i2Rθ2π⇒1π=θ2π⇒θ=2rad
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A wire carrying current i has the configuration shown in figure. Two semi-infinite straight sections, each tangent to the same circle, are connected by a circular arc, of angle θ, along the circumference of the circle, with all sections lying in the same plane. What must θ (in rad) be in order for B to be zero at the center of circle?