An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d a). If the loop applies a force F on the wire then :

Question

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d > > a). If the loop applies a force F on the wire then : (A) F propto ((a2/d3)) (B) F propto ((a/d)) (C) F propto ((a/d))2 (D) F = 0

Tardigrade Admin · Accepted Answer

Eqvilent dipole of given loop F =m . (dB/dr) Now (dB/dx) = (d/dx) ((μ0I/2π x)) propto(1/x2) ⇒ textSo F propto (M/x2) [∵ M = NIA] ∴ F propto(a2/d2)

Q. An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is $d (d >> a)$ . If the loop applies a force $F$ on the wire then :

$F \propto (\frac{a ^{2}}{d ^{3}})$

$F \propto (\frac{a}{d})$

$F \propto (\frac{a}{d})^{2}$

$F = 0$

Eqvilent dipole of given loop
$F = m . \frac{d B}{d r}$
Now $\frac{d B}{d x} = \frac{d}{d x} (\frac{μ _{0} I}{2 π x})$
$\propto \frac{1}{x ^{2}}$
$\Rightarrow So F \propto \frac{M}{x ^{2}} [∵ M = N I A]$
$∴ F \propto \frac{a ^{2}}{d ^{2}}$

Q. An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d(d>>a). If the loop applies a force F on the wire then :

F∝(d3a2​)

F∝(da​)

F∝(da​)2

F=0