Question

The magnetic field on the axis of a current-carrying circular coil of radius a at a distance 2a from its centre will be

• A. $\frac{{\mu }_{0}i}{2}$
• B. $\frac{{\mu }_{0}i}{10\sqrt{5a}}$
• C. $\frac{{\mu }_{0}i}{4a}$
• D. ${\mu }_{0}i$

Answer 1

The correct option is B $\frac{{\mu }_{0}i}{10\sqrt{5a}}$

The magnetic field on the axis of a current-carrying circular coil of radius $r$ at a distance $d$ from its center is given by
$B=\frac{{\mu }_{0}I{r}^2}{2(d^2+r^2{)}^{3/2}}$
Here, $r=a$ and $d=2a$, hence
$B=\frac{{\mu }_{0}I{a}^2}{2(2a^2+a^2{)}^{3/2}}$
$B=\frac{{\mu }_{0}I{a}^2}{2(5a{)}^{3/2}}$
$B=\frac{{\mu }_{0}I{a}^2}{2\left(5{)}^{3/2}\right(a^2{)}^{3/2}}$
$B=\frac{{\mu }_{0}I}{2\left(\sqrt{2}5\right)\left(\sqrt{5}\right)a}$
$B=\frac{{\mu }_{0}I}{10\left(\sqrt{5}a\right)}$