Am I correcting in assuming a strong enough magnetic field would be able to shield the crew?
Yes, but, you'd need one of stupendous strength. Something on the order of 20 Tesla (about 400,000x the strength of Earth's magnetic field.) And you'd probably require two such fields. One to shield the crew from the incoming cosmic rays, and another of the opposite polarity to shield to crew from the first (as moving around inside static magnetic fields of a mere 0.5 Tesla is enough to cause electrolysis of saliva and other notable biological effects.)
To generate such a field would, by one estimate I've read, require some nine tons of superconducting cable, its associated cryogenic cooling, and the rigid structures required to keep said cables in place.
Why would you need such a strong field. A much weaker field protects on Earth
The effectiveness of shielding depends on the strength of the magnetic field and the thickness of that field. The product of the two determines how far the particles are deflected - to shield effectively the radiation needs to be deflected around the outside of the body in question.
The earth has a weak field that extends for a long distance!
I dont think a field as strong as 20 Tesla is needed. NASA are investigating shields in the region of 1 to 10 Tesla of varying thicknesses to see what is most effective. Planning to use high temperative superconducting magnets.
Their initial research indicates lower strength but thicker fields may be the way to go.
See here
http://www.nasa.gov/directorates/spacet ... ction.html