Magnetic Effects Of Current Question 2
Question 2 - 24 January - Shift 1
A circular loop of radius $r$ is carrying current I A. The ratio of magnetic field at the centre of circular loop and at a distance $r$ from the center of the loop on its axis is :
(1) $1: 3 \sqrt{2}$
(2) $3 \sqrt{2}: 2$
(3) $2 \sqrt{2}: 1$
(4) $1: \sqrt{2}$
Show Answer
Answer: (3)
Solution:
Formula: Magnetic field due to circular loop
Magnetic field due to current carrying circular loop on its axis is given as
$\frac{\mu_0 ir^{2}}{2(r^{2}+x^{2})^{3 / 2}}$
At centre, $x=0, B_1=\frac{\mu_0 i}{2 r}$
At $x=r, B_2=\frac{\mu_0 i}{2 \times 2 \sqrt{2} r}$
$\frac{B_1}{B_2}=2 \sqrt{2}$
