Question

The magnetic field due to a current in a straight wire segment of length $L$ at a point on its perpendicular bisector at a distance $r (r >> L)$

• A. decreases as $\frac{1}{r}$
• B. decreases as $\frac{1}{r^{2}}$
• C. decreases as $\frac{1}{r^{3}}$
• D. approaches a finite limit as $r \to \infty$

Answer 1

Answer: (B)

decreases as $\frac{1}{r^{2}}$

Answer 2

By Biot-Savart's law, the magnetic field due to a current carrying wire is
$B=\frac{\mu_{0}}{4 \pi} \cdot \frac{I d l \sin \theta}{r^{2}}$
So, $B \propto \frac{1}{r^{2}}$
So, the magnetic field due to current decreases as inverse square of distance of the point of observation.