Question

A circular coil of radius ‘r’ carries a current I. At what distance from centre on its axis the magnetic field is $\frac{1}{27}th$ of its value at the centre?

• A. $\sqrt{3}r$
• B. $2\sqrt{2}r$
• C. $2\sqrt{3}r$
• D. $\sqrt{5}r$

Answer 1

The correct option is B $2\sqrt{2}r$

$B_a=\frac{1}{27}{B}_c\frac{{\mu }_{0}ni{r}^2}{2[r^2+x^2{]}^{3/2}}=\frac{1}{27}\frac{{\mu }_{0}ni}{2r}{r}^3=\frac{1}{3^3}[r^2+x^2{]}^{3/2}$
$r=\frac{1}{3}[r^2+x^2{]}^{1/2}{r}^2=\frac{1}{9}[r^2+x^2]9r^2-r^2=x^{2}x=\sqrt{8r^2}x=2\sqrt{2}r$