# Quick question on direction of dl in motional emf integral

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1. May 20, 2015

### edsoneicc

1. The problem statement, all variables and given/known data
u = velocity
B = magnetic flux density

2. Relevant equations
∫ (uxB)⋅dl

3. 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?

2. May 21, 2015

### 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.