TBR Electrostatics and Magnetism Q's

[sigle]

I just had a few questions on this section. If anyone can help me better understand whats going on here I would be so grateful.

The attached image is very similar to the one given in the passage. Passage talks about dragging a conducting rod through a magnetic field induces an emf between the ends of the bar. This emf then drives a current through circuit, which produces its own magnetic field that opposes the initial flux.

Question 6. If the rod in the Figure is released with zero velocity, and if the rails on which the rod sits are frictionless, the rod will:
A. Not move when a current is running through the resistor.
B. move to the left, to minimize the area of the circuit loop.
C. move to the right, to max. the magnetic flux through the circuit loop.
D. remain stationary, to keep the magnetic flux through the circuit loop constant.

So I guessed D and got it right BUT I dont know what's going on here

OKay I understand whats going on until it gets to flux. When they are talking about flux does it increase as its being dragged through the field? The passage gives the eqn for flux as <greek symbol (Fi)> = BA. I figured that neither of the field and area was changing therefore flux was constant. But I'm not entirely sure about that. If someone can explain whats going on here it would be extremely helpful.

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[lorenzomicron]

Well, if the rod is at zero velocity, then it won't move unless a force is applied by newton's first law. as the rod is a conductor, there is no charge buildup; as there is no charge, the magnetic/electric field can not affect the bar. thus, there is no force. thus, there will be no increase in magnetic flux.

alternatively, if the bar did have some velocity, then the bar would move and the area of the space would increase, because the bat keeps increasing the length of the rectangle as it moves. this would cause some current to flow in that circuit.