Question

A circular loop of radius R is carrying current I. The ratio of magnetic field at the center of circular loop and at a distance R from the center of the loop on its axis is

• A. \(1:\sqrt{2}\)
• B. \(1:3\sqrt{2}\)
• C. \(\sqrt{8}:1\)
• D. \(3\sqrt{2}:1\)

Hint:

Use the on-axis formula with x equal to R.

Answer 1

The Correct Option is C

Step 1: Ratio formula
$\frac{B_c}{B_x} = \left(1+\frac{x^2}{R^2}\right)^{3/2}$.

Step 2: Evaluate
With $x=R$, $2^{3/2} = 2\sqrt2 = \sqrt8$. Option (C).

Final Answer:
root 8 : 1. \[ \boxed{\text{(C)}\ \sqrt8:1} \]