Question

The magnetic field at the center of a circular current-carrying loop of radius $R$ is $B$. The field at a point on the axis at a distance $R$ from the center is:

• A. $B/\sqrt{2}$
• B. $B/2$
• C. $B/2\sqrt{2}$
• D. $B/8$

Hint:

The axial field decreases as you move away from the center of the loop.

Answer 1

The Correct Option is C

Step 1: Concept
$B_{axis} = B_{center} \times \frac{R^{3}}{(R^{2} + x^{2})^{3/2}}$.
Step 2: Analysis
Given $x = R$. $B_{axis} = B \times \frac{R^{3}}{(2R^{2})^{3/2}} = B \times \frac{R^{3}}{2\sqrt{2} R^{3}}$.
Step 3: Conclusion
$B_{axis} = B / 2\sqrt{2}$.
Final Answer: (C)