# Conducting slidewire see system-Faraday's Law

1. May 5, 2015

### Gemma95

1. The problem statement, all variables and given/known data

A conducting slidewire system is set up as shown. The sliding wire has mass m and electrical resistance R and falls under gravity as shown. The fixed wire loop has zero resistance and lies perpendicular to a uniform magnetic field B shown pointing into the page.
i) Use Faraday's Law to determine the maximum velocity of the slidewire.
ii) How much power is dissipated at the peak velocity?

2. Relevant equations

ɛ=-dФ/dt
P=(I^2)R

3. The attempt at a solution
I defined the area vector as pointing in the same direction as the magnetic field, so
ɛ=-B(dA/dt)
In time dt the slidewire moves a distance vdt, giving ɛ=-BLv where L is the width of the slidewire.
I think I am simplifying the problem too much by simply rearranging for v in this equation and obtaining
v=-ɛ/BL -should I differentiate in order to maximise v? I feel I am missing something by not including the given mass m.

For the second part, overall current I=|ɛ|/R, so I=BLv/R
P=I^2R=(BLv/R)^2/R

P(dissipated)=(B^2L^2v^2)/R

Thanks in advance for any help, much appreciated.

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2. May 5, 2015

### BvU

But with v=-ɛ/BL you haven't determined v yet, have you !?

Is there something that stops you from answering e.g. $v = -{\tfrac 1 2} g t^2$ ?

Not so certain my help has helped. Can you enlighten me ?

Last edited: May 6, 2015