Question

The magnetic field at the center of a circular current carrying conductor of radius $r$ is $B_c$. The magnetic field on its axis at a distance $r$ from the center 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)

$2\sqrt{2}:1$

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 $B_a=\frac{{\mu }_{o}I{r}^2}{2(x^2+r^2{)}^{3/2}}$ where $x=r$

$\therefore$ $B_a=\frac{{\mu }_{o}I{r}^2}{2(r^2+r^2{)}^{3/2}}$

Or $B_a=\frac{{\mu }_{o}I}{2r}.\frac{1}{2\sqrt{2}}$

$⟹$ $B_c:B_a=2\sqrt{2}:1$