Wires $1$ and $2$ carrying currents ${i_1}$ and ${i_2}$respectively are inclined at an angle $\theta $ to each other. What is the force on a small element $dl$ of wire $2$ at a distance of $r$ from wire $1$ (as shown in figure) due to the magnetic field of wire $1$
AIEEE 2002,AIIMS 2013, Medium
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(c) Length of the component dl which is parallel to wire $(1)$ is $dl\cos \theta $, so force on it.
$F = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2{i_1}{i_2}}}{r}(dl\cos \theta ) = \frac{{{\mu _0}{i_1}{i_2}dl\cos \theta }}{{2\pi r}}$
$F = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2{i_1}{i_2}}}{r}(dl\cos \theta ) = \frac{{{\mu _0}{i_1}{i_2}dl\cos \theta }}{{2\pi r}}$
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