Question

The magnetic field at the centre of a circular coil of radius \( R \) carrying current \( I \) is 64 times the magnetic field at a distance \( x \) on its axis from the centre of the coil. Then the value of \( x \) is

• A. \( \frac{R}{\sqrt{5}} \)
• B. \( \frac{R}{3} \)
• C. \( \frac{R}{4} \)
• D. \( \frac{R}{\sqrt{3}} \)

Answer 1

The Correct Option is A

The magnetic field at the center of a circular coil is given by:
\( B_{\text{center}} = \frac{\mu_0 I}{2R} \)

The magnetic field at a point along the axis of the coil at a distance \( x \) is:
\( B_x = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}} \) 

Given that the magnetic field at the center is 64 times the magnetic field at distance \( x \), we use the relation:
\( B_{\text{center}} = 64 B_x \) 
By solving the equation, we find:\( x = \frac{R}{\sqrt{5}} \)