Quick question on direction of dl in motional emf integral

[edsoneicc]

Homework Statement

u = velocity
B = magnetic flux density

Homework Equations

∫ (uxB)⋅dl

The Attempt at a Solution

From my understanding, the direction of dl depends on the resulting direction of (uxB). How will I know if my dl is in positive or negative?

 

[BvU]

Hi Ed,

Little response so far eh? Perhaps because there is no problem statement ? And your equation isn't an equation ?
Attempts at solution usually look different also.

On the constructive side: in something like$$
X =\int_a^b (...) \cdot \vec {dl}$$ the direction of $l$ is established by the path to be followed from $\vec a$ to $\vec b$ : positive is towards $\vec b$.

Since $\vec u \times \vec B$ is generally perpendicular to $\vec u$, and $\vec u$ is generally along $\vec {dl}$, the dot product is generally zero: magnetic fields have a tendency to change the direction of velocities but not the magnitude.