Question

A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r < R) from its centre

• A. $B∝r^2$
• B. $B∝r$
• C. $B∝\frac {1}{r^2}$
• D. $B∝\frac {1}{r}$

Answer 1

Answer: (B)

$B∝r$

Answer 2

We know that,
$∫B.dl = μ_0l_{in}$
$B \times 2\pi r = \frac {μ_0l}{\pi R^2} \times \pi r^2$
$⇒ B ∝ r$

So, the correct option is (B): $B ∝ r$