The induced electromotive force generated between the two intersections of the metal bar and the guide rail is E=BLv, and the obtained electromotive force changes with the change of l; The resistance of the loop is R=Lr.

Then I=ER=BLvLr=Bvr according to the ohm's law of closed circuit, so I is unchanged, so A is wrong and B is right.

C, metal bar uniform motion, external force and ampere force balance, there are:

F=BIL, which means that F varies with L, so C is wrong.

D, the thermal power of the induced current P=I2R=I2Lr, and if l changes, p also changes, so d is wrong.

So choose: B.