Question

A long straight wire of radius $R$ carries a steady current, $I_0$, uniformly distributed throughout the cross-section of the wire. The magnetic field at a radial distance $r$ from the center of the wire, in the region $r > R$, is

• A. $\dfrac{\mu_0 I_0}{2\pi r}$
• B. $\dfrac{\mu_0 I_0}{2\pi R}$
• C. $\dfrac{\mu_0 I_0 R^2}{2\pi r}$
• D. $\dfrac{\mu_0 I_0 r^2}{2\pi R}$
• E. $\dfrac{\mu_0 I_0 r^2}{2\pi R^2}$

Hint:

Outside the wire, treat current as concentrated at the center.

Answer 1

The Correct Option is A

Concept:
Outside a current-carrying wire: \[ B = \frac{\mu_0 I}{2\pi r} \]

Step 1: Region $r > R$.
Entire current is enclosed.

Step 2: Apply Ampere's law.
\[ B(2\pi r) = \mu_0 I_0 \]

Step 3: Solve.
\[ B = \frac{\mu_0 I_0}{2\pi r} \]