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  4. A circular coil carrying a certain current produces a magnetic field Bo at its centre. The coil is now rewound so as to have 3 turns and the same current is passed through it. The new magnetic field at the centre is

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Q. A circular coil carrying a certain current produces a magnetic field $B_o$ at its centre. The coil is now rewound so as to have $3\, turns$ and the same current is passed through it. The new magnetic field at the centre is

KCETKCET 2007Moving Charges and Magnetism

Solution:

The magnetic field produced at the centre of the circular coil carrying current is given by
$Bv = \frac{\mu_0 NI}{2r}$
For one turn$ N = 1 $
$B_0 = \frac{\mu_0 I}{2r}$
As the coil is rewound
$r' = \frac{r}{3} , N' = 3$
$B' = \frac{\mu_0I \times 3}{2 \times \left( \frac{r}{3} \right)}$
$= \frac{9 \mu_0I }{2r} = 9B_0$