Calculating Motional EMF when v not perpendicular to B

[vaizard]

Hi,

I'm trying to figure out how you can calculate motional EMF when the velocity of the object in question is not perpendicular to the magnetic field. There are two equations in my textbook, but the text describing them is not very helpful.

The first is $$\varepsilon = vBL$$, which can be used when $$B\perp v$$ and $$B\perp L$$. The second is $$\varepsilon = \oint (\vec v \times \vec B) \cdot d\vec l$$ which is the general form. The first one won't work if they're not perpendicular, and I don't understand what the $$d\vec l$$ is for in the second one. Could someone explain that to me?

Thanks!

 

[tiny-tim]

… I don't understand what the $$d\vec l$$ is for in the second one. Could someone explain that to me?

Hi vaizard!

v x B is the magnetic force vector

dl is a short length of the wire

the force won't necessarily be along the wire, so (v x B).dl is the component of force along the wire