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 center 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. \( \frac{a}{2}, 3a \)
• B. \( \frac{a}{2}, 2a \)
• C. \( \frac{a}{4}, 2a \)
• D. \( \frac{a}{4}, \frac{3a}{2} \)

Hint:

The magnetic field inside a wire increases linearly with distance from the center, while outside the wire, it follows the same pattern as that for a point charge.

Answer 1

The Correct Option is C

For a straight wire with a uniform current distribution, the magnetic field inside the wire is proportional to the distance from the center, and the magnetic field outside the wire behaves as if all the current were concentrated at the center. To find the distance where the magnetic field is half of the maximum field, we solve the appropriate equations for magnetic field strength inside and outside the wire, yielding distances \( \frac{a}{4} \) and \( 2a \).