Explaining F=BIl and F=Bqv for Many Charges

[poojarao]

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

 

[Gear300]

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.

 

[poojarao]

thanks a lot!

 

[Bob S]

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.

 

[Born2bwire]

The I/v vectors need not be orthogonal with the B vector.