Question

The ratio of the magnetic fields at the centre of a circular coil carrying current to that at a point whose distance is half of the radius of the coil is:

• A. $2\sqrt{5}:8$
• B. $5\sqrt{5}:8$
• C. $5\sqrt{5}:4$
• D. $2\sqrt{5}:4$

Answer 1

The correct option is B $5\sqrt{5}:8$

$\frac{B_C}{B_X}=\frac{{(r^2+x^2)}^{3/2}}{r^3}=\frac{{(r^2+\frac{r^2}{4})}^{3/2}}{r^3}=\frac{{\left(\frac{5}{4}{r}^2\right)}^{3/2}}{r^3}={\left(\frac{5}{4}\right)}^{3/2}=\frac{5\sqrt{5}}{8}$