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Find the magnetic field at the centre of...

Find the magnetic field at the centre of the circular loop shown in figure.

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Magnetic field at the point O due to infinite wire is `(mu_(0)i)/(2piR)` out of the plane.
Magnetic field at the point O due to circular loop is `(mu_(0)i)/(2R)` into the plane
Thus net field `= (mu_(0)i)/(2R) [(1)/(pi) hat(k) - hat(k)]`
`= (mu_(0)i)/(2R) [(1)/(pi) - 1] hat(k)`
`= (mu_(0)i)/(2R) ((pi -1)/(pi)) (-hat(k))`
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