Flux increase due to velocity?

I have a book question I'm trying to understand:

The first bit is easy enough. The second part I was confused so I checked the solution:

B is into the page. The flux increases as the bar moves to the right, so the magnetic field of the induced current is out of the page inside the circuit. To produce magnetic field in this direction the induced current must be counterclockwise, so from b to a in the rod.

I thought I had a pretty good grip on increasing/decreasing magnetic field inducing negative/positive current(respectively). Maybe I'm missing something real trivial but I don't understand how flux increases as the bar moves. Why?

• You can think of this circuit abcd increasing the size as if it was made from stretchable wires. Then the magnetic flux through the circuit increases since the circuit becomes larger, so the induced current has to oppose the increase of the flux. Another way to solve this problem is by considering the Lorentz force on charge carrying particles (electrons in metal) in the moving bar ab. – Maxim Umansky Nov 7 '13 at 7:02