Figure here shows three cases, in all cases the circular path has radius r and straight ones are infinitely long. For same current, the magnetic field at the center P in cases (1), (2) and (3) have the ratio
Text Solution
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For first figure,
Magnetic field at P due to straight part , 
Magnetic field at P due to circular part , 
Magnetic field at P due to straight part ,
So, net magnetic field at the center of first figure,
… (i)
For second figure, magnetic field at P due to two straight and one circular part,
… (ii)
For third figure, magnetic field at P due to straight part ,
Magnetic field at P due to circular part ,
Magnetic field at C due to straight part , 
So, net magnetic field at centre of third figure,
… (iii)
From Eqs. (i), (ii) and (iii), we get
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