What is the magnetic induction of the field at the point O due to a current carrying wire that has the shape as shown in the figure?
The radius of the curved part of the wire is R, the linear parts are assumed to be very long.

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$\frac{μ_{0} I}{4 π R} [2 + π]$

$\frac{μ_{0} I}{4 π R} [2 + \frac{3 π}{2}]$

$\frac{μ_{0} I}{4 π R} [1 + \frac{π}{2}]$

$\frac{μ_{0} I}{4 π R} [1 + \frac{3 π}{2}]$

answer is D.

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Detailed Solution

Magnetic field at centre 'O'

$B_{o} =$ Magnetic field due to straight wires + magnetic field due to circular wire

$= 0 + \frac{μ_{0} I}{4 π r} + \frac{3 μ_{0} I}{8 R}$

$∴ B_{0} = \frac{μ_{0} I}{4 π R} (1 + \frac{3}{2} π)$

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