An infinitely long straight current carrying wire produces a magneti field B, at a point distance 'a' from it. What must be the radius of a circular circular loop, so that, for the same current through it, the magnetic field at its centre equals B/2 and an axial point, distance equal to the radius of the loop, equals, B?
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The field at point O will be the resultant of the fields due so circular loop and straight wire. So, the field due to both the loop and the wire at centre O will be out of the page.
The magnetic field at the centre (O) of the loop.
B=4πμ0R2I+4πRμ02πI
⇒B=4πμ0R2I[1+π]
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