When you look at the right side of the diagram, as it starts to rotate it will move down and to the left. The movement down has no effect as it is in the direction of the field. So the movement left is what will induce a current. The induced current will result in a force pushing right and B is down so the current is out of the page, from right hand palm rule.
Other way of doing it is, as the coil starts to spin the magnetic flux is decreasing. From Lenz's law the induced current needs to increase the flux again. To do this the magnetic field in the coil must be increased. So grab a section of the coil with your right hand, so the fingers are going down inside the coil and your thumb points in the direction of the current.
Other way of doing it is, as the coil starts to spin the magnetic flux is decreasing. From Lenz's law the induced current needs to increase the flux again. To do this the magnetic field in the coil must be increased. So grab a section of the coil with your right hand, so the fingers are going down inside the coil and your thumb points in the direction of the current.
