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 a

Question

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 :

TestHub · Accepted Answer

Magnetic field at the centre of the coil is given by, $B = \frac{μ_{0} i}{2 R}$ .

Now in the first case:

$B = 4 (\frac{μ_{0} i}{2 R})$

and for the second case:

$B' = \frac{μ_{0} i}{2 R'}$ .

As the length of the wire will remain same, therefore

$2 π R' = 4 (2 π R) \Rightarrow R' = 4 R$

Hence, required ratio will be

$\frac{B'}{B} = \frac{R}{4 R^{'}} = \frac{1}{16}$

$\Rightarrow B' = 2 T$

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