Question

The magnetic field at the centre of a circular current carrying conductor of radius $r$ is $B_c$. The magnetic field on its axis at a distance $r$ from the centre is $B_a$. The value of $B_c:B_a$ will be

• A. $1:\sqrt{2}$
• B. $1:2\sqrt{2}$
• C. $2\sqrt{2}:1$
• D. $\sqrt{2}:1$

Answer 1

Answer: (C)

Magnetic field at the center of the circular current carrying loop $B_c=\frac{{\mu }_{o}I}{2r}$ Magnetic field at a distance $r$ on the axis
$B_a=\frac{{\mu }_{0}I{r}^2}{2{\left(x^2+r^2\right)}^{3/2}}$ where $x=r$
$\therefore B_a=\frac{{\mu }_{0}I{r}^2}{2{\left(r^2+r^2\right)}^{3/2}}$
Or $B_a=\frac{{\mu }_{o}I}{2r}\cdot \frac{1}{2\sqrt{2}}$
$⟹B_c:B_a=2\sqrt{2}:1$