Well, essentially shields are forcefields by any other name and they've been used in a variety of different applications in various Trek episodes from defensive, to containment, to structural integrity.I think enveloping the barge in the Enterprise's shields was done to reinforce its hull integrity.
Well, they slap on the shields after it proves impossible to use the bolt-on thrusters, and necessary to use the tractor beam. This might be in order to keep the barge from falling apart (although we don't learn of any mechanism by which shields could achieve that, here or in any other episode), or in order to keep radiation from spreading out.
Given that no order was given to drop the shields around the barge, it seems that they remained around it during the flight.We don't know whether the shields remain extended around the barge after they clear the planet's vicinity...
Which is really why the use of the shields to help keep the otherwise disintegrating barge together is the most plausible idea. They certainly weren't for protecting the Enterprise from the radiation (wouldn't it have been better not to stretch them around the barge in that case?) and if they weren't considered necessary for going through the asteroid field in the original plan....we only know the shields remain up, we don't hear how they are configured.
And we don't hear they would be used to protect the barge from asteroid strikes (which would admittedly be silly - surely our heroes could dodge the rocks with ease, even with the barge in tow? Indeed, the whole point of the exercise was that the ship would actively tow the barge through the belt, and at that point it wouldn't be for speed of getting it away from the planet. It would be purely for allowing the barge to negotiate a course it could not negotiate by coasting.).
I believe in the above transcript, LaForge was simply stating their current situation while thinking what options were available to him in regards to the tractor beam. But it can also be looked at as being a case that they had one system (a tractor beam) operating within another (the deflector shields) and that latter was having an impact on the former.Yet we have this bit of dialogue:
Riker: "Geordi, you've got to stabilise that tractor beam."
LaForge: "I can't divert any more power to the shields."
If the transcript is correct, tractor beam gets more stable if power is diverted to the shields... Why, beats me, but there we have it - it does seem as if the shields indeed exist in order to stabilize the towing arrangement somehow.
If that was truly the case, it really wouldn't have been necessary to get rid of the barge. They could have merely positioned it at any point clear of the planet and left it there indefinitely.our heroes couldn't just leave it out there to dissipate on its own
Why not? If it took three thousand years, ships could be told to steer clear of the barge for three thousand years, and that would be it.
But--and I believe this to be most likely--it was a case that they wanted an environmentally-free system (no irradiated zones or spacelanes), then getting completely rid of the barge was the thing to do. It just turned out to be more troublesome than they thought it would be and dangerous than they liked it to be.