The words "barbed wire" on a comment really jumped out at me. NO ONE recommends using barbed wire with goats because they have very thin skin compared to cattle, and it could do some serious damage to them. Some goats won't respect electric, which is why it's best to not even bother trying. Woven wire works fine for fencing in Nigerians, although I keep my bucks behind livestock panels if there are does in a neighboring pasture. There are a lot of conversations in the forum archives about fencing and housing.
The way that would work is if they where pretty close together, and not all the high tensile wire would have to be hot..maybe have one 6-8 inches off the ground be hot, next one ground wire then another hot one, then another ground and a hot one at the top all about 6-8 inch spaces... thats five wires. You may luck out and they stay in.... Mine are not the tamest things in the world and would rush the fence... then i would wet the ground and them they stopped that.. with them being wet they REALLY get a jolt.
Sounds like you have a great plan there! I would expect at least one to figure out the weak spot! They may not be as smart as chimps but never underestimate the little turds! If the hot wire is running the inside of a large fence then they should not mess with it. They will be grounded good when they hit both fence should give then a good "think about it" jolt. I have seen one lady use barbed wire for the "discouraging" of the rubbing. I laughed at it but they never had one rub on the woven cattle wire they had! Guess it hurt too bad... course it was very sharp barbs.
Electric fence works and sometime it don't... the little goats really have very little respect for it... I watch them make a run for it and go right under it. My boer cross will NOT try it... he goes around LOL. Right now I have my buck in part cattle panels part hog panels.. if he tries and figures it out he may get out.... They will go UNDER anything.. fence HAS to be solid when they push it won't give. 6 to 8 inches off of ground... they can flatten out pretty good. I have my does in a 6 foot wooden corral we made for horses... slats are about 10 inch spaced... so far Wild has jumped it.. she will jump 4 foot like it is nothing....
How long have you raised goats? After 14 years with pygmys.... the only full proof confinement is a enclosed stock trailer! I use 5 foot cattle panels to keep the adults in but the babies go through... I have 4 foot hog panels and have some adults that just flat foot jump over and never touch the top and babies will jump up and squeeze through the larger top holes. If you want to pay big bucks, horse panels are the best fencing for the small goats... nothing will go through those and they cant tear them up rubbing on them. Welded wire will get ruined due to the rubbing. You would have to put a post ever 2 feet IF that would even keep the fence tight.
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2-quart milk pail
Mineral feeder (put minerals in one side and baking soda in the other!)