In article , "dusty "
says...

How close to power lines in the attic can network cable be without causing interference.

You need to worry more about lightning strikes..

Keep the wire far enough away so that if your power likes
do get hit, the strike can not make it over to your network
cables.

That's not to say that your devices connected to the grid
won't get hit so what ever

At least 6 inches or more I would say for that, as for basic
line noise, you can get close to the wores.

Network cables are twisted pairs so they are design to reduce
external noise to a degree.

Jamie