Question

The magnetic induction at a point at a large distance d on the axial line of circular coil of small radius carrying current is 120 $\mu T$. At a distance 2d the magnetic induction would be:

• A. 60$\mu T$
• B. 30$\mu T$
• C. 15$\mu T$
• D. 240$\mu T$

Answer 1

The correct option is C 15$\mu T$

The magnetic field at a point at a distance d on the axial line of circular coil of radius r is given by , $B=\frac{{\mu }_{0}I{r}^2}{2(r^2+d^2{)}^{3/2}}$

So, $B=\frac{{\mu }_{0}I{r}^2}{2\left[d^2\right(1+r^2/d^2){]}^{3/2}}=\frac{{\mu }_{0}I{r}^2}{2d^3}(1+r^2/d^2{)}^{-3/2}=\frac{{\mu }_{0}I{r}^2}{2d^3}(1-3a^2/2d^2+...)$

We get $B=\frac{{\mu }_{0}I{r}^2}{2d^3}$

(As $d>>r$ so higher order term can be negligible)

Thus, $\frac{B_{2d}}{B_d}=\frac{d^3}{(2d{)}^3}$

or $B_{2d}=B_d/8=120/8=15\mu T$