The field B at the centre of a circular coil of radius r is π times that due to a long straight wire at a distance r from it, for equal currents here shows three cases; in all cases the circular part has radius r and straight ones are infinitely long. For same current the field B is the centre P in cases 1, 2, 3 has the ratio
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Case 1: 
◉ ◉
◉ ◉
So net magnetic field at the center of case 1
⇒ ⇒ 
◉ ◉ ..... (i)
Case 2: As we discussed before magnetic field at the center O in this case
.....(ii)
Case 3: 
◉ ◉
So net magnetic field at the center of case 3
....(iii)
From equation (i), (ii) and (iii) 
◉ ◉ : π π ◉ ◉ : 
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