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Question

The net magnetic force on the conducing wire per unit length

$\mathrm{F}=\int 2 \mathrm{dF} \cos 	heta$

$=\int 2\left[\frac{\mu_{0}(\mathrm{d}

Vedclass · Accepted Answer

$\frac{{{\mu _0}i{i_0}}}{{{\pi ^2}R}}$

Vedclass · Answer

The net magnetic force on the conducing wire per unit length

$\mathrm{F}=\int 2 \mathrm{dF} \cos 	heta$

$=\int 2\left[\frac{\mu_{0}(\mathrm{d} i) i_{0}}{2 \pi \mathrm{R}}ight] \cos 	heta$

$=\frac{\mu_{0} i_{0}}{\pi R} \int d i \cos 	heta$

where,

$\mathrm{d} i=\frac{i}{\pi \mathrm{R}} 	imes \mathrm{R} \mathrm{d} 	heta=\frac{i \mathrm{d} 	heta}{\pi}$

$	herefore \,\,\, \mathrm{F}=\frac{\mu_{0} i_{0}}{\pi \mathrm{R}} \int \frac{(i \mathrm{d} 	heta) \cos 	heta}{\pi}$

$=\frac{\mu_{0} i_{0} i}{\pi^{2} \mathrm{R}} \int_{0}^{\pi / 2} \cos 	heta \mathrm{d} 	heta=\frac{\mu_{0} i_{0} i}{\pi^{2} \mathrm{R}}$

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