## Moving a rectangular prism through a magnetic field

1. The problem statement, all variables and given/known data
The figure shows a metallic block, with its faces parallel to coordinate axes. The block is in a uniform magnetic field of magnitude 0.020 T. One edge length of the block is 25 cm; the block is not drawn to scale. The block is moved at 2.8 m/s parallel to each axis, in turn, and the resulting potential difference V that appears across the block is measured. With the motion parallel to the y axis, V = 18 mV. With the motion parallel to the z axis, V = 0 mV. With the motion parallel to the x axis, V = 12 mV.

2. Relevant equations
F{b} = |q|v X B
F{e} = Eq
E = V / d

3. The attempt at a solution
I have no idea where I'm wrong.

B/c V = 0 when the motion is parallel to the z axis, I know the direction of the magnetic field is parallel to the z axis.

So when the metal is moved parallel to the y axis, the magnetic force F{b} is parallel to the x axis.

So the conduction electrons in the metal are pushed in either the -x or x direction until the electric force produced by the separation of charges is equal to the magnetic force, and equilibrium is reached.

This will mean that the electric potential on either the "right" or "left" face of the rectangular prism is greater than the electric potential on the opposite face.

This means there is a voltage across the distance between them.

This means there is a voltage across the distance marked d$$_{x}$$.

This means that, after setting F{b} = F{e} and solving and substituting to get:

qvB = Eq
qvB = (Vq)/d
d = V/(vB)

I can say that d$$_{x}$$ = .018 / (2.8*0.02) = .32m.

But the truth is d$$_{y}$$ = .018 / (2.8*0.02) = .32m.

Why in the world is this?
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