Free fall of straight wire in a homogeneous magnetic field

[alkmini]

hello every body. I have a high school problem
a straight horizontal wire is falling freely in a homogeneous horizontal magnetic field, perpendicular to the wire and i want to find the inductive voltage.
I said E= Blv=Blgt
But I can also say E=ΔΦ/Δt=BΔΑ/Δt=Βl1/2gt [t][2]/Δt=1/2Blgt
why doew this difference of 1/2 arise?

 

[lluke9]

Hummm...

Your problem arises because of something like this:v = gt, but... v = 1/2gt too?

That's because on the first equation, you were finding INSTANTANEOUS velocity, so therefore INSTANTANEOUS EMF.
On the second equation, you somehow got average velocity... I'm still trying to figure it out.

A-ha! Okay, I think I got it figured out.
When you substituted 1/2gt for X, and divided by t to get 1/2gt, you actually found the average velocity, since it's NOT instantaneous velocity. The velocity constantly changes because the wire is accelerating.

Both of your equations are right, except the first one is instantaneous EMF after a certain T, and the second equation is average EMF with respect to T.

 

[alkmini]

thanks a lot