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A current I flows around a closed path i...

A current I flows around a closed path in the horizontal plane of the circle as shown in the figure. The path consists of eight arcs witli alternating radii r and 2r.
Each segment of arc subtends equal angle at the common centre P. Find the magnetic field produced by current path at point P

Text Solution

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B due to straight parts of the wire is zero. Each arc subtends an angle
`theta = (2pi)/(8) = pi //4`
`therefore B_("net") = 4 ((mu_0 I)/(4pi r) xx pi//4) + 4 ((mu_0 I)/(4pi (2r)) xx pi // 4 )`
` = (3 mu_0 I)/(8r)`, perpendicular to the plane fo the paper and directed inward.
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