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)

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 (1/r) (B) decreases as (1/r2) (C) decreases as (1/r3) (D) approaches a finite limit as r → ∞

Tardigrade Admin · Accepted Answer

By Biot-Savart's law, the magnetic field due to a current carrying wire is

B = \frac{μ _{0}}{4 π} \cdot \frac{I d l s i n θ}{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.

Q. 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 $r (r >> L)$

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

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

decreases as $\frac{1}{r ^{3}}$

approaches a finite limit as $r \to \infty$

By Biot-Savart's law, the magnetic field due to a current carrying wire is
$B = \frac{μ _{0}}{4 π} \cdot \frac{I d l s i n θ}{r ^{2}}$
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.

Q. 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)

decreases as r1​

decreases as r21​

decreases as r31​

approaches a finite limit as r→∞