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  4. The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

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Q. The electric current in a circular coil of four turns produces a magnetic induction $32 \,T$ at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

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Solution:

$ B =\frac{\mu_0 i }{2 R } \times 4 $
$ B ^{\prime} =\frac{\mu_0 i }{2 R ^{\prime}} $
$R ^{\prime} =4 R$
$ B ^{\prime} =\frac{\mu_0 i }{8 R } $
$ \frac{ B ^{\prime}}{ B } =\frac{1}{16} $
$ B ^{\prime} =2 T $