Question

A long straight wire of radius \( R \) carries current \( i \). The magnetic field inside the wire at distance \( r \) from its centre is expressed as:

• A. \( \frac{\mu_0 i}{\pi R^2} r \)
• B. \( \frac{2 \mu_0 i}{\pi R^2} r \)
• C. \( \frac{\mu_0 i}{2 \pi R^2} r \)
• D. \( \frac{\mu_0 i}{2 \pi r} \)

Hint:

The magnetic field inside a current-carrying conductor increases linearly with distance from the center, proportional to \( r \).

Answer 1

The Correct Option is B

Step 1: Magnetic Field Inside a Conductor.
For a current-carrying wire of radius \( R \), the magnetic field at a distance \( r \) from the center (inside the wire) is given by: \[ B = \frac{\mu_0 i}{2 \pi R^2} r \] where \( r \) is the distance from the center of the wire, and \( R \) is the radius of the wire.
Step 2: Conclusion.
The correct answer is (B), \( \frac{2 \mu_0 i}{\pi R^2} r \).