- #1
KleZMeR
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Homework Statement
There is a rectangular loop submerged in uniform magnetic field, where all but one edge is in the field, and I am given W (length), Bo, R (resistance), L (self-inductance), m.
I am to find v(t), y(t), and i(t). when R = 0 and L =/ 0 (L is NOT =0)
Homework Equations
Fnet = m(dv/dt) = Fexternal - Fmagnetic
Fexternal = mg
Emfinduced = Vinduced= -(dflux/dt) = v*B*W
Fmagnetic = Iinduced*W*Bo
flux=L*I
Emfinduced = -L*(dI/dt)
The Attempt at a Solution
So I think the result is that two parallel sides with induced currents in opposite directions will cancel out, and only one side, length W will contribute to force, because if total loop was submerged into B field region then force would be zero.
And, so, I solved this for the conditions R=/0 and L = 0 (R is NOT =0), so I have not included any equations with R because I am not using it, so what I am trying to do is solve it in similar fashion as before, using the equation of motion.
So I think I am to use again the Fmagnetic = Iinduced*W*Bo
What I am having trouble with is finding Fmagnetic in terms of Iinduced in terms of the given variables.
I see that there is an equation relating flux to Iinduced, as well as Emfinduced to Iinduced
I'm not using the flux equation, because I don't see a differential area, because I am dealing with a wire here, or do I use the differential area covered by the whole rectangle even though there is no contribution from the two parallel wires?
My guess would be to again use:
Fmagnetic = Iinduced*W*Bo
and (dI/dt) = (vBoW/L) = (dy/dt)*(BoW/L)
and then divide out dt, because current over a change in time is not a current?
so I get:
(dI) = (dy)*(BoW/L)
and so then I = y*(BoW/L)
and then use:
m(dv/dt) = Fexternal - Fmagnetic = mg - (y*(BoW/L)*WBo)
and integrate?
but I don't know if I can do this...
any help would be graetly appreciated