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

Engineering

Physics

Magnet and Magnetic Dipole

Question

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

F = 0

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

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

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Force on one pole

$F = \frac{{mμ}_{0} I}{2 π \sqrt{d^{2} + x^{2}}}$ m = pole

Strength

Total force = 2F sin θ

$= \frac{2 \times μ_{0} Im \times x}{2 π \sqrt{d^{2} + a^{2}} \sqrt{d^{2} + a^{2}}} = \frac{μ_{0} Imx}{π | d^{2} + a^{2} |}$

= m²x = M = I πa²

^{$Total force = \frac{μ_{0} {Ia}^{2}}{2 (d^{2} + a^{2})}$}

^{$\approx \frac{μ_{0} {Ia}^{2}}{2 d^{2}}$ $[∵ d > > a]$}