- #1
beborche
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Homework Statement
There's a magnetic field B in +[itex]\hat{z}[/itex]. A rectangular loop is lying in the xy-plane. Three sides are static, the 4th one is moving with velocity v along the direction of +[itex]\hat{y}[/itex], making the rectangular larger and larger. The length of this moving side of the rectangle is L.
Determine an expression for the magnitude of the electromotoric voltage induced in the loop using the flux through the loop.
Homework Equations
1. [itex]\Phi[/itex]m=[itex]\int[/itex]BdS
2. ε=-[itex]\frac{∂\Phi}{∂t}[/itex]
3. s = v*t (s = displacement, v = velocity, t=time)
The Attempt at a Solution
Using 1) and 3), with dS=dxdy[itex]\hat{z}[/itex] I get
[itex]\Phi[/itex]m=[itex]\int[/itex]BdS = B[itex]\int[/itex][itex]\int[/itex]dxdy (with limits x:0→L and y:0→y0+v*t) = ... = BL(y0+v*t) = BLy0 + BLvt
Then using 2)
ε=-[itex]\frac{∂\Phi}{∂t}[/itex] = -[itex]\frac{∂}{∂t}[/itex](BLy0 + BLvt) = -Bvl
Everything here is correct, except the sign in the end. It should, apparently, not be negative. It should be positive, i.e. just Bvl, not -Bvl. I don't understand why. In the answers, the only thing that differs from my solution is their definition of dS. They define it as dS=dxdy(-[itex]\hat{z}[/itex]) instead of dS=dxdy[itex]\hat{z}[/itex]. I don't understand why they define it in (-[itex]\hat{z}[/itex]). Can anyone shed some light on this, please?