Question

If a current \( I \) is flowing in a loop of radius \( r \) as shown in the adjoining figure, then the magnetic field induction at the center O will be

• A. Zero
• B. \( \frac{\mu_0 I}{4 \pi r} \)
• C. \( \frac{2 \mu_0 I}{4 \pi r} \)
• D. \( \frac{\mu_0 I}{2 \pi r} \)

Hint:

The magnetic field at the center of a current-carrying loop can be derived using Ampère's law and is proportional to the current and inversely proportional to the radius.

Answer 1

The Correct Option is B

Step 1: Applying Ampère's law.
The magnetic field induction at the center of a loop carrying a current is given by Ampère’s law. For a circular loop, the magnetic field is \( \frac{\mu_0 I}{4 \pi r} \), where \( r \) is the radius of the loop.

Step 2: Conclusion.
The correct magnetic field induction at the center is \( \frac{\mu_0 I}{4 \pi r} \), which corresponds to option (2).