An infinite straight current carrying conductor is bent in such a way that a circular loop is formed on it as shown in the figure. If the radius of the loop is R, the magnetic field at the centre of the loop is .

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Accepted Answer

(4) (μ₀)/(4π)·(2I)/R(π+1). Given: an infinite straight wire with a circular loop of radius R formed on it; the wire touches the loop, so the centre is a perpendicular distance R from the wire. Idea: superpose the two fields at the centre, the loop's and the straight wire's. Loop: B₁=(μ₀ I)/(2R). Straight wire: B₂=(μ₀ I)/(2π R). In the figure the current runs round the loop in the sense that makes both fields point out of the plane of the paper, so they add. B=(μ₀ I)/(2R)+(μ₀ I)/(2π R)=(μ₀ I)/(2π R)(π+1)=(μ₀)/(4π)·(2I)/R(π+1).

An infinite straight current carrying conductor is bent in such a way that a circular loop is formed on it as shown in the figure. If the radius of the loop is R, the magnetic field at the centre of the loop is ______.

Step-by-step solution

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