Question

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 $3turns$ and the same current is passed through it. The new magnetic field at the centre is

• A. $3Bo$
• B. $\frac{B_0}{3}$
• C. $9B_0$
• D. $\frac{B_0}{9}$

Answer 1

Answer: (C)

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
$r^{\prime }=\frac{r}{3},N^{\prime }=3$
$B^{\prime }=\frac{{\mu }_{0}I\times 3}{2\times \left(\frac{r}{3}\right)}$
$=\frac{9{\mu }_{0}I}{2r}=9B_0$