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From Wikipedia's Europa (moon); Orbit and rotation:
Europa orbits Jupiter in just over three and a half days, with an orbital radius of about 670,900 km....and is tidally locked to Jupiter, with one hemisphere of Europa constantly facing Jupiter.
Question: Since at least the ice crust of Europa is locked to Jupiter, wouldn't the far side be way less irradiated and always facing away from Jupiter?
The radiation that causes problems near Jupiter is not emitted by Jupiter. Jupiter has radiation belts, like Earth's Van Allen belts, but much more intense. This radiation doesn't consist of photons, but high-velocity ions - electrons, protons, and maybe some larger nuclei. They are captured mostly from the solar wind and accelerated by their interaction with the magnetic field of Jupiter.
When I think of radiation I tend to think of something that moves in a straight line, but high-velocity ions are considered to be radiation too, and they curve when they're in a magnetic field. That's why you can have belts of radiation around a planet. So there is no perfect shadow like you would have if the problem consisted of gamma rays (which are photons and do move in straight lines) emitted from Jupiter.
I have not been able to find good information about the closest you could approach Jupiter in an unshielded spacecraft for (say) hours without getting an unacceptable dose. But that would be a different question.
