Question

a circular coil of radius r carries curent i another coil of radius 2r carries current i the magnetic field at the centro of the two coils is

Answer 1

The magnetic field at a distance axially $x$ from the center of a current carrying loop of radius $r$ is

$B(x)=\frac{\mu_0I}{2} \frac{r^2}{(x^2+r^2)^{3/2}}$.

The magnetic field at the center of the coil is

[tex] B(0)=\frac{\mu_0I}{2} \frac{r^2}{(0^2+r^2)^{3/2}}\\

B(0)=\frac{\mu_0I}{2} \frac{r^2}{r^3}\\

B(0)=\frac{\mu_0I}{2r} [/tex]

Assume that the currents are in the same direction (clockwise or anticlockwise) in both the coils.

Also assuming the two coils are coaxial and co-planar, the magnetic field at the center of the two coils is

$B(0)=\frac{\mu_0I}{2r}+\frac{\mu_0I}{4r}\\ B(0)=\frac{3\mu_0I}{4r}$