Recall that the Force vecF experienced by a charged particle of charge q moving with velocity vec v in a magnetic field vecB is given by the relation
vecF=q(vecvxxvecB)
We also know that
velocity vecv="displacememt"/"time"
If the charge moves through distance =length vecL in time t
vecv=vecL/t. Inserting in the force equation we obtain
vecF=q(vecL/txxvecB)
Rearranging scalar quantities we get
vecF=q/t(vecLxxvecB)
=>vecF=I(vecLxxvecB), where q/t=I is the current flowing in the wire.
You may use the expression vecF=|vecL|(vecIxxvecB) knowing well that the direction of vecI and vecL is same.
However, we must appreciate that direction of vecL defines the direction of vecI. Perhaps and not vice versa.
