Question

A current passing through a circular coil of two turns produces magnetic field $B$ at its centre. The coil is then produces magnetic field $B$ at its centre. The coil is then rewound so as to have four turns and the same current is passed through it. The magnetic field at its centre now is

• A. $2B$
• B. $\frac{B}{2}$
• C. $\frac{B}{4}$
• D. $4B$

Answer 1

The correct option is D $4B$

$B=\frac{{\mu }_0}{4\pi }\frac{2\pi nI}{r}$ i.e. $B\propto \frac{n}{r}$;

Given, $L=2\pi r_1\times 2=2\pi r_2\times 4;\frac{r_1}{r_2}=\frac{4}{2}=2$

$\frac{B_2}{B_1}=\frac{n_2}{n_1}\times \frac{r_1}{r_2}=\frac{4}{2}\times 2=4$

or $B_2=4B_1=4B$