How is F=BIl the same as F=Bqv for many charges?

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poojarao
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Speed = distance/time and current = charge/time. Explain how F=BIl is actually the same equation as F= Bqv but considered for many charges in a group?

can someone please explain with working out please?

thanks
 
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Lets say that you had a wire with a length l. Let's say that traveling through that length is a net charge q, with an average velocity of v. v = distance/time, in which in this case, v = l/t. The current is I = charge/time = q/t. Therefore, F = B*q*(l/t) = B*(q/t)*l = BIl.
 
For clarity, these two equations (part of the Lorentz Force Law) are written as

F = l(I x B) = q(v x B)

where x indicates the cross product. meaning that the vectors F,I and B; or F,v,and B are all mutually orthogonal.