Question

The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the Centre is 54 $\mu T$. What will be its value at the centre of loop?

Answer 1

r=3 cm

Magnetic field due to current loop (n=1) at a distance x=0.04 m from the centre on the axis is

$B=\frac{{\mu }_0}{4\pi }\frac{2\pi nI{r}^2}{(r^2+x^2{)}^{3/2}}$

$\Rightarrow I=\frac{540\times (0.05{)}^3}{2\pi \times (0.03{)}^2}$

Magnetic field at the centre of the loop is,$B=\frac{{\mu }_0}{4\pi }\frac{2\pi nI}{\left(r\right)}=250\mu T$