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

The Correct Option is C

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