What is the magnetic field at the center of the following ring of current?

• A. μ₀i/(2r)
• B. μ₀i/(πr²)
• C. μ₀i/(2πr)
• D. μ₀i / √(2πr)

Answer: (A)

Verified step by step guidance

1. Identify the problem: We need to find the magnetic field at the center of a circular loop carrying a current i. The radius of the loop is r.
2. Recall the formula for the magnetic field at the center of a circular loop: The magnetic field B at the center of a loop of radius r carrying a current i is given by B = (μ₀i)/(2r), where μ₀ is the permeability of free space.
3. Understand the direction of the magnetic field: According to the right-hand rule, if the current flows in a counterclockwise direction, the magnetic field at the center points out of the plane of the loop.
4. Compare with the given options: The correct formula for the magnetic field at the center of the loop is μ₀i/(2r), which matches one of the provided options.
5. Conclude the solution: Based on the formula and the options given, the correct answer is μ₀i/(2r).