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Magnetic Force on Current Carrying Wire

A wire of len...

Question

A wire of length $l$ carries a current $i$ along the x-axis.A magnetic field $\to B = B_{o} (^j +^k)$ exists in the space.Find the magnitude of the magnetic force acting on the wire.

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Solution

$\to I = l^i$
Now, $\to F = i (\to I \times \to B)$
$= i [(l^i) \times (B_{o}^j + B_{o}^k)]$
$= i l B_{o} (^k -^j) = | \to F | = \sqrt{2} i l B_{o}$

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