Question

A long straight rod of diameter 4 mm carries a steady current \( i \). The current is uniformly distributed across its cross-section. The ratio of the magnetic fields at distances 1 mm and 4 mm from the axis of the rod is.

• A. 8:1
• B. 1:4
• C. 4:1
• D. 1:1 \bigskip

Hint:

The magnetic field produced by a current-carrying wire is inversely proportional to the distance from the wire.

Answer 1

The Correct Option is D

Step 1: The magnetic field at a distance \( r \) from a long straight conductor is given by Ampère's law: \[ B = \frac{\mu_0 i}{2 \pi r} \] The ratio of the magnetic fields at distances 1 mm and 4 mm is: \[ \frac{B_1}{B_2} = \frac{\frac{\mu_0 i}{2 \pi (1 \, \text{mm})}}{\frac{\mu_0 i}{2 \pi (4 \, \text{mm})}} = \frac{1}{1} = 1:1 \] Thus, the ratio of the magnetic fields is \( \boxed{1:1} \). \bigskip