Question

A circular coil of n turns and radius r carries a current l. the magnetic field at the centre is

• A. $\frac{{\mu }_{0}nI}{r}$
• B. $\frac{{\mu }_{0}nl}{2r}$
• C. $\frac{2{\mu }_{0}nI}{r}$
• D. $\frac{{\mu }_{0}nI}{4r}$

Answer 1

The correct option is B $\frac{{\mu }_{0}nl}{2r}$

Solution: As we know that,

magnetic field due to circular coil having $n$ turns and

of radius $r$ and carries a current $I$ is at distance x,

$B=\frac{{\mu }_{0}nI{r}^2}{2(r^2+x^2{)}^{3/2}}$ $...\left(1\right)$

At centre: $x=0$

so,$e{q}^n\left(1\right)$becomes,

$B=\frac{{\mu }_{0}nI{r}^2}{2(r^2{)}^{3/2}}$

$B=\frac{{\mu }_{0}nI{r}^2}{2r^3}$

$B=\frac{{\mu }_{0}nI}{2r}$

hence,

The correct opt: B