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A wire of length l metre carries a curre...

A wire of length l metre carries a current I ampere along the Y-axis. A magnetic field, `vecB=B_0(hati+hatj+hatk)` tesla exists in space. Find the magnitude of the force on the wire.

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As the wire carries current I along the y-axis, so `vecl=lhatj`. Magnetic force on wire is
`vecF=I(veclxxvecB)=I[lhatjxx[B_0(hati+hatj+hatk)])`
`=IlB_0[hatjxxhati+hatjxxhatj+hatjxxhatk]`
`=IB_0[-hatk+0+hati]=IlB_0[hati-hatk]`
Magnitude of the magnetic force is
`F=IlB_0[(1)^2+(-1)^2](1//2)=IlB_0sqrt2N`
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