Question

Consider a long straight wire of a circular cross-section (radius \( a \)) carrying a steady current \( I \). The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field (inside the wire, outside the wire) is half of the maximum possible magnetic field, anywhere due to the wire, will be:

• A. \( \left[ \frac{a}{2}, 3a \right] \)
• B. \( \left[ \frac{a}{2}, 2a \right] \)
• C. \( \left[ \frac{a}{4}, 2a \right] \)
• D. \( \left[ \frac{a}{4}, \frac{3a}{2} \right] \)

Hint:

For a uniformly current-carrying wire, the magnetic field inside increases linearly with the radial distance, and outside it decreases with distance. Use Ampère’s Law to derive such relationships.

Answer 1

The Correct Option is C

The magnetic field inside a current-carrying wire increases linearly with the distance from the center. The maximum magnetic field occurs at the surface, and the magnetic field is half of this maximum value at the point where the distance is \( \frac{a}{4} \) inside the wire and at \( 2a \) outside the wire. Thus, the correct answer is \( \left[ \frac{a}{4}, 2a \right] \).