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.
