I have been working on an habitable moon orbiting a gas giant about 3 times the mass of jupiter and lately I have been having issues assessing how the giant's magnetosphere may affect it. To give you an idea of the situation the moon orbits at a distance that allows for a 36 hours long orbital period, so about 544477 kms and has a comfy atmosphere abundant with greenhouse and shielding gases.
My main concerns are: with the moon orbiting at that distance, how likely is that it the gas giant's magnetic field could irradiate it to a point that it would become inospitable? And if that is so, what measures do I need to take in order to avoid it?
On that note I figured that by inclining the moon's orbit to the planet's plane by about 5 to 10 degrees the moon would be able to avoid intersecting the gas giant's magnetotail thus avoiding the brunt of the irradiation. Would that be helpful?
And on another note, can the magnetic field be a problem to the development of an advanced civilization on this moon? And if it is a problem, what measures can be taken to lessen it's ill effects?
I personally thought about the moon itself having a magnetic field thanks to it's molten, irony core, thus essentially providing a bit of additional shielding, but I am not too sure, do you think it would help/be possible?
A little addendum. I envisioned the planet to have a biosphere pretty similar to earth's. With complex organisms, the five kingdoms and intelligent humanoids. The main differences that I thought about would be: an abundance of plantlife and forests across most of the planet's surface and kelp forests in the waters (60-65% of the planet would be underwater), animals living there would be cancer resistant.