No. Perhaps it's 1.5 mm^2, which would be 7/0.52 mm, or an old imperial size (pre-1970) but I'd expect 3/0.029" in that case.
No, because of voltage drop over that length. What's the socket for? For the gate opener alone you could use a 6A MCB in which case the cable would be OK. If you really need a 16 A circuit (13 A socket + 3 A gate motor) then you'll need 4 mm^2 cable.
You might want to think about the earthing arrangements for the gate, especially if the house supply is PME.
It's less than 0.52 - my calipers say 0.50 and my micrometer says
0.020" = 0.508. I rounded to 0.48 as it matched 1.25mm!
I need to run a car vac or a pressure washer, so about 1KW max, and not at the same time as the gate. I've opted for a 10A MCB, as that's all I could get on eBay (old MK Sentry).
Yes, on PME. Would another earth rod be a good idea? However, if you are going to tell me to isolate the earth, I'm going to ignore you ;-)
You need to feed through a 30mA RCD at the house end. Earth the cable armour at the house end in the normal way and *isolate* it at the gate end. Provide a suitable earth electrode for earthing the gate and socket (resistance to earth should be < 1.6k ohm and preferably less than 200 ohm).
If you do not do this then should the combined neutral and earth (CNE) feed to the house become o/c your gate will be live at full phase voltage (not protected by the RCD) which is a trifle dangerous. OK, on an urban supply the risk of this is very low, but not zero. The risk is higher on rural overhead supplies.
An alternative strategy would be to export the house earth via the armour and provide the lowest resistance earth electrode system you can manage, connected to the main earth terminal in the house (suggest 2 or
3 rods each sunk to 8 or 12 ft.) That would help reduce the touch voltage at the gate in the case of the o/c CNE feed. The RCD is still required, because of the socket provided for portable equipment outdoors.
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