Question

A circular coil carrying a certain current produces a magnetic field $B_0$ 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

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

Answer 1

The correct option is B $9B_0$

Let initial radius is $r$.
So, $2\pi r=3\times 2\pi r_1$
$⟹r_1=\frac{r}{3}$
Initially $B_0=\frac{H_{0}I}{2r}$
Finally $B=\frac{H_0\left(3I\right)}{2r_1}=9\frac{H_{0}I}{2r}$
$=9B_0$