Potential difference between 2 points in a wire carrying induced current

I came across this problem in my physics book. It states that if we were to have a wire AB moving perpendicularly upwards to a magnetic field going into page, as shown in the figure, which point, A or B, would have higher potential difference?

x x x x x x x x

x x x x x x x x

X A---------B x

x x x x x x x x

x x x x x x x x

According to Fleming right hand rule, current in this wire will be induced from B to A and normally, current moves from higher voltage to lower one, which means that voltage at A is lower than B. This wire would act though like a DC battery should it be connected to an external resistor, making the voltage at A higher than B!

The wire is acting as a source and so the induced current (Fleming's right hand rule) inside it will go from the negative (lower potential $B$) to the positive (higher potential $A$). This would mean that is connected to an eternal circuit the current would flow from the positive terminal to the negative terminal.