GCE physics?

Question

mangetic force on a current-carrying wire F = BILsinθ
magnetic force on a moving charge F = BQvsinθ
what is the relationship between the 2 equations?
i mean how to derive 1 equation from the other & vice versa
hope sb can answer it~~ thx a lot

Answer 1

We have = B I Lsinθ
and
F = B Q v sinθ

We know that current I is a a rate of flow of charge Q
I=Q/t t=Q/I

We know that speed is length L over time
v=L/t

since t=Q/I
we have v= LI /Q

substituting into
F=B Q L I/ Q sin(θ)
and since Q cancels out we have
F= B L I sin(θ)

Does that help?