When is the force experienced by current carrying conductor placed in a magnetic field largest ?

Explanation

Consider a rod of uniform cross-sectional area A and length `l`.
Let the number density of mobile charge carriers (of each charge q) in it be n.
Then the total number of mobile charge carriers in it is nAl.
For a steady current I in this conducting rod, each mobile carrier has an average drift velocity `vec(v_(d))`.
In the presence of an external magnetic field `vec(B)`, the force on these carriers is `vec(F)=(nAl)q[vec(v_(d))xxvec(B)]`.
But nq `vec(v_(d))=vec(j)`, is the current density and `|(nq vec(v_(d)))|A=I` is the current.
Thus, force on the conductor
`vec(F)=[(nqvec(v_(d)))Al]xx vec(B)=[vec(j)Al] xx vec(B)= I ( vec(l) xx vec(B))`
Where `vec(l)` is a vector of magnitude l, the length of the rod, and with a direction identical to the current I.