Question

The magnetic field at the centre of a current loop of radius \(r\) carrying a current \(I\) is

• A. \(\frac{\mu_0 I}{2r}\)
• B. \(\frac{\mu_0 I}{r}\)
• C. \(\frac{\mu_0 I}{\pi r}\)
• D. \(\frac{2\mu_0 I}{r}\)
• E. \(\frac{\mu_0 I}{2\pi r}\)

Hint:

For a circular arc subtending an angle \(\theta\) at the center, \(B = \frac{\mu_0 I}{4\pi r} \theta\) (with \(\theta\) in radians). For a full loop, \(\theta = 2\pi\), giving \(B = \frac{\mu_0 I}{2r}\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a standard formula for the magnetic field at the center of a circular current-carrying loop.

Step 2: Detailed Explanation:
The magnetic field at the center of a circular loop of radius \(r\) carrying a current \(I\) is given by: \[ B = \frac{\mu_0 I}{2r} \] where \(\mu_0\) is the permeability of free space. The direction is perpendicular to the plane of the loop (right-hand rule).

Step 3: Final Answer:
The magnetic field is \(\frac{\mu_0 I}{2r}\).