Shielded Ethernet cable questions

Hi everyone,

I would like to replace our standard Ethernet cable with something better. I will try to be brief in describing the situation.

We have:

1 cable modem
2 computers
1 four port wired router

It all functions fine; except, the blue Ethernet cable carries a high electric field, as well as emits RF noise (I can even pick it up with an AM radio at several or more inches).

I want a wired solution which will allow us to share our internet connection between the computers using the modem and router we have, but without the cable carrying an electric field (which I can only assume is being carried along from the router/modem, which of course are plugged into AC power)...

...and don't want the Ethernet cable to emit any RF. I'm more concerned with RF that's coming *out* of the Ethernet cable than what can pass *in* to it.

As far as the RF goes, I'm going to assume that it's being inducted (is that the right word?) from the information being processed in the modem and router, and is itself the data from the internet simply functioning. (The router, and especially modem emit a lot of RF, very audible with an AM radio, and also use what I guess are switching power supplies, adding to the noise).

So, I'd considered using multimode fiber optics...until I found out that I'd need a media converter at each end of the fiber optic cable! One at the router, one at my computer!

Simplified, my goal is to be as low in all electromagnetic radiation from all components as possible. Since this is what I'd like to achieve, using media converters for fiber optic cable wouldn't have a point for me, because they, themselves, are powered by wall-wart type AC-DC transformers, which generate strong magnetic fields, and a lot of RF noise.

What I'm trying to figure out is, will "shielded" Ethernet cable prevent the outward radiation of all RF noise generated by the data traveling along the cable?

I see MHz ratings given to a lot of shielded Ethernet cable; what does that rating mean? It's always a single number.

Assuming that shielded cable will prevent the outward radiation of all RF, can I further prevent the transfer of RF onto the shielded Ethernet cable from the modem or router by using shielded connectors such as this?:

http://sewelldirect.com/RJ45e-8P8C-S...ectors-100.asp

Is this size, RJ45, standard? As in, the same plug that normal, commercial Ethernet cable uses to connect to computers, routers, modems?

Would ferrite clamps help, too?

Now, if all the RF shielding I want can be accomplished by using shielded Ethernet cable, the next question is this:

How can I prevent the transfer of the electric field from the AC powered modem and router from carrying all the way along the Ethernet cable?

(I know that's what it's from, rather than the Ethernet cable picking up electric fields from other wiring - I checked when the router was unplugged and there was no e-field on the Ethernet cable; plugged the router back in and the e-field on the Ethernet cable jumped way up).

A tech on the phone told me that it shouldn't induct the electric field, but the connection was wonky, and he or I may have misunderstood eachother; if a cable's shielding relies on conductive material, that would mean that an electric field would be, well, conducted!

Is there a way around this? Can a conducted electric field be contained at its source, so it doesn't follow a cable?
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Please bear in mind that I'm not more technically knowledgeable than it seems by what I've posted. If anyone has suggestions how to proceed, can clarify if "shielded" cable actually entails that RF won't come out of the cable, how to further prevent RF from the router and modem from getting on the cable, which cable type to actually look for, and how to deal with the electric field, it would be hugely appreciated.

Thank you!