cheers John
,
As a sparks I sort of have to say that power to a barn really should be installed by a qualified person with the right test equipment, as there are questions about the suitability of the earthing system of your installation for outdoor/livestock areas; installation and verification of earth rod(s) at the barn and whether or not the cable needs to be RCD protected or not - which cannot be answered without visiting the site and looking and testing.
if the 'barn' is essentially an indoor area with a dry nonconducting floor (e.g. suspended floorboards, not concrete on earth) and there are no 'extraneous conductive parts' like metal pipes or structural steel, and/or there's no livestock then it may not be such an issue.
As for the cable- As John says the cable needs to be mechanically protected - that doesn't
have to be armoured cable but the question is how much protection your proposed conduit provides, especially if it's not buried 2 or three feet down out of harms way.
It is allowable to run a cable along a fence as it's visible and can be avoided, but you have to consider the risks of the location (tractors/lorries turning / animals chewing).
I generally find that armoured is as cheap or cheaper than the alternatives anyway (buy online - google it), and if/when the cable is breached, it's certainly safer to have a cable surrounded by an earthed steel screen than just having an extra layer of plastic (the armour of the SWA must always be earthed).
There's a useful calculator here for cable sizes you can play with:
http://www.tlc-direct.co.uk/Technical/Charts/VoltageDrop.htmlwhich will tell you the cable you need to comply with building regs (3% v drop for lights and 5% for other loads IIRC) and will also tell you what the designated cables current carrying capacity is.
But if you plan to use a fan heater (2kw) and a kettle (say 2.4) and you don't want the lights to dim when the kettle / heater are turned on then I think it'll tell you you'll be wanting 16mm 3 core SWA.
If you disregard building regs and don't mind the lights dimming a bit when the kettles on you could get away with 10mm, and if you're willing to unplug the heater when boiling the kettle you might even get away with 4mm, but if someone comes along and plugs in a big compressor or something the lights may dim a lot. NB if you have a 13A socket on the end of the cable then the minimum load you should specify for the calc is 3.1 kw regardless of what you're planning on plugging in - unless you put a fuse/MCB on the upstream end of the cable to limit it to less that this.
If you are going to be naughty and do it yourself (which I don't recommend) then make sure that everything is protected by a 30mA RCD (including the cable) as a minimum precaution.
if you do go for a weedy cable and your office ends up with a fridge and a computer, you may find your computer doesn't like the voltage dips when the fridge turns on - they draw quite a surge on startup.