Question

A circular coil of wire of radius $r$ has $n$ turns and carries a current $l$. The magnetic induction ($B$) at a point on the axis of the coil at a distance $\sqrt{3}r$ from its centre is

• A. $\frac{{\mu }_{0}In}{4r}$
• B. $\frac{{\mu }_{0}In}{8r}$
• C. $\frac{{\mu }_{0}nI}{16r}$
• D. $\frac{{\mu }_{0}In}{32r}$

Answer 1

The correct option is C $\frac{{\mu }_{0}nI}{16r}$

$B=\frac{n{\mu }_{0}i{a}^2}{2(a^2+x^2{)}^{3/2}}$
$=\frac{n{\mu }_{0}I{r}^2}{2(r^2+3r^2{)}^{3/2}}$
$=\frac{n{\mu }_{0}I{r}^2}{2\times 8\times r^3}$
$=\frac{{\mu }_{0}nI}{16r}$