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Two long wires, carrying currents i1 an...

Two long wires, carrying currents ` i_1 and i_2,` are placed perpendicular to each other in such a way that they just avoid a contact. Find the magnetic force on a small length dl of the second wire situated at a distance l from the first wire. (figure)

Text Solution

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The situation is shown in figure.The magnetic field at the site of `dl` due to the first wire is `B=(mu_(0)i_(1))/(2pil)`
This field is perpendicular to the plane of the figure going into it.The magnetic force on the length `dl` is,
`dF=i_(2)dlB sin 90^(@)= (mu_(0)i_(1)i_(2)dl)/(2pil)`
This force is parallel to the current `i_(1)`
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