Question

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field $B_1$ at its centre when a current $I$ passes through it. The second wire is bent into a coil with free identical loops adjacent to each other and produces magnetic field $B_2$ at the centre of loops with current $I/3$ passing through it. The ratio $B_1:B_2$

• A. $1:1$
• B. $1:3$
• C. $1:9$
• D. $9:1$

Answer 1

The correct option is B $1:3$

Magnetic field due to circular current carrying arc

$B=\frac{{\mu }_0}{4\pi }\frac{2\pi i}{r}=\frac{{\mu }_{0}i}{2r}$

magnetic field at axis due to circular current carrying wire -

$B_{axis}=\frac{u_0}{4\pi }\frac{2\pi Ni{r}^2}{(x^2+r^2{)}^{3/2}}$

$B_1=\frac{{\mu }_{0}I}{2\alpha }$