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|dw:1361068864225:dw|
Is that what it means?

|dw:1361069290883:dw|

Why would E be in the direction from a to b?

Well, it could be the other way, but usually a is initial and b is final...

a positive test charge will move from a to b if the field points from a to b

I see......!!!!|dw:1361069892440:dw|

oops
because of\[\vec E\cdot\vec r=\|\vec E\|\|\vec r\|\cos\theta\]

Sorry I didn't quite get that....
which way does the r vector point? tangent to the path?

yeah that makes sense. cos 90 is zero....